------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.

from a 12-square array ( 4 x 3 sheet )

How many 2-stamp combinations can you create ?
How many 3-stamp combinations can you create ?
How many 4-stamp combinations can you create ?

Each of the 2,3,4 stamps must be connected by an edge

for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped

On 25/10/2022 05:23, henh...@gmail.com wrote:
>
> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
>
>
>
> from a 12-square array ( 4 x 3 sheet )
>
> How many 2-stamp combinations can you create ?
> How many 3-stamp combinations can you create ?
> How many 4-stamp combinations can you create ?
>
>
>
> Each of the 2,3,4 stamps must be connected by an edge
>
> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
>

What do you count as separate combinations? Are rotated/translated combinations distinct?

Mike.

On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> On 25/10/2022 05:23, henh...@gmail.com wrote:
> >
> > ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> >
> >
> >
> > from a 12-square array ( 4 x 3 sheet )
> >
> > How many 2-stamp combinations can you create ?
> > How many 3-stamp combinations can you create ?
> > How many 4-stamp combinations can you create ?
> >
> >
> >
> > Each of the 2,3,4 stamps must be connected by an edge
> >
> > for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> >

> What do you count as separate combinations? Are rotated/translated combinations distinct?
>
> Mike.

we can assume that each stamp in the (X times Y) sheet has a different picture.

for me ... i'm most curious if there's an answer that comes out simply as
e.g.
(x-1)C(z-1) times (y-1)C(z-1)

___________________
Rereading Proust produces a state of mental inertia (6)

On 25/10/2022 17:35, henh...@gmail.com wrote:
> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
>> On 25/10/2022 05:23, henh...@gmail.com wrote:
>>>
>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
>>>
>>>
>>>
>>> from a 12-square array ( 4 x 3 sheet )
>>>
>>> How many 2-stamp combinations can you create ?
>>> How many 3-stamp combinations can you create ?
>>> How many 4-stamp combinations can you create ?
>>>
>>>
>>>
>>> Each of the 2,3,4 stamps must be connected by an edge
>>>
>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
>>>
>
>
>> What do you count as separate combinations? Are rotated/translated combinations distinct?
>>
>> Mike.
>
>
> we can assume that each stamp in the (X times Y) sheet has a different picture.
>
>
> for me ... i'm most curious if there's an answer that comes out simply as
> e.g.
> (x-1)C(z-1) times (y-1)C(z-1)

Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.

All the answers are like that, but we have to appropriately account for rotations/reflections, and
the different shapes that are included in the set to be counted.

So... for 4-stamp combinations: (with a 4x3 sheet)

h v rr Tot

xxxx : 1 x 3 x 1 = 3

x : 4 x 0 x 1 = 0
x x
x

xxx : 2 x 2 x 4 = 16
x

xx : 3 x 1 x 4 = 12
x
x

xxx : 2 x 2 x 2 = 8
x

x : 3 x 1 x 2 = 6
xx
x

xx : 3 x 2 x 1 = 6
xx

xx : 2 x 2 x 2 = 8
xx

x : 3 x 1 x 2 = 6
xx
x

Total: 65

[ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]

If you're saying you would like a simple formula to get the final number 65, there is not going to
be any such 'simple' formula. For a single shape, the formula is simple, but making different
shapes is not simple...

If you want to vary just the width/height of the sheet, then the number 65 above varies in the
obvious way, as the h and v columns adjust, so we could get a simple formula for this (a polynomial
of degree 2 in W,H), at least for W,H >= 4. (For smaller W,H, some shapes may not fit at all,
complicating things.)

Mike.
ps. there may be silly mistakes in above calculation!

On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
> On 25/10/2022 17:35, henh...@gmail.com wrote:
> > On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> >> On 25/10/2022 05:23, henh...@gmail.com wrote:
> >>>
> >>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> >>>
> >>>
> >>>
> >>> from a 12-square array ( 4 x 3 sheet )
> >>>
> >>> How many 2-stamp combinations can you create ?
> >>> How many 3-stamp combinations can you create ?
> >>> How many 4-stamp combinations can you create ?
> >>>
> >>>
> >>>
> >>> Each of the 2,3,4 stamps must be connected by an edge
> >>>
> >>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> >>>
> >
> >
> >> What do you count as separate combinations? Are rotated/translated combinations distinct?
> >>
> >> Mike.
> >
> >
> > we can assume that each stamp in the (X times Y) sheet has a different picture.
> >
> >
> > for me ... i'm most curious if there's an answer that comes out simply as
> > e.g.
> > (x-1)C(z-1) times (y-1)C(z-1)
> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
>
> All the answers are like that, but we have to appropriately account for rotations/reflections, and
> the different shapes that are included in the set to be counted.
>
> So... for 4-stamp combinations: (with a 4x3 sheet)
>
> h v rr Tot
>
> xxxx : 1 x 3 x 1 = 3
>
> x : 4 x 0 x 1 = 0
> x
> x
> x
>
> xxx : 2 x 2 x 4 = 16
> x
>
> xx : 3 x 1 x 4 = 12
> x
> x
>
> xxx : 2 x 2 x 2 = 8
> x
>
> x : 3 x 1 x 2 = 6
> xx
> x
>
> xx : 3 x 2 x 1 = 6
> xx
>
> xx : 2 x 2 x 2 = 8
> xx
>
> x : 3 x 1 x 2 = 6
> xx
> x
>
> Total: 65

i got 65 too.

> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
>
> If you're saying you would like a simple formula to get the final number 65, there is not going to
> be any such 'simple' formula.

i'd love to see a simple formula for this (or similar) problem.

__________________________

from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?

Assuming that the ans. here is 65...

from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?

---------- is it bigger or smaller than 6500 ?

On 28/10/2022 21:19, henh...@gmail.com wrote:
> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
>> On 25/10/2022 17:35, henh...@gmail.com wrote:
>>> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
>>>> On 25/10/2022 05:23, henh...@gmail.com wrote:
>>>>>
>>>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
>>>>>
>>>>>
>>>>>
>>>>> from a 12-square array ( 4 x 3 sheet )
>>>>>
>>>>> How many 2-stamp combinations can you create ?
>>>>> How many 3-stamp combinations can you create ?
>>>>> How many 4-stamp combinations can you create ?
>>>>>
>>>>>
>>>>>
>>>>> Each of the 2,3,4 stamps must be connected by an edge
>>>>>
>>>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
>>>>>
>>>
>>>
>>>> What do you count as separate combinations? Are rotated/translated combinations distinct?
>>>>
>>>> Mike.
>>>
>>>
>>> we can assume that each stamp in the (X times Y) sheet has a different picture.
>>>
>>>
>>> for me ... i'm most curious if there's an answer that comes out simply as
>>> e.g.
>>> (x-1)C(z-1) times (y-1)C(z-1)
>> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
>>
>> All the answers are like that, but we have to appropriately account for rotations/reflections, and
>> the different shapes that are included in the set to be counted.
>>
>> So... for 4-stamp combinations: (with a 4x3 sheet)
>>
>> h v rr Tot
>>
>> xxxx : 1 x 3 x 1 = 3
>>
>> x : 4 x 0 x 1 = 0
>> x
>> x
>> x
>>
>> xxx : 2 x 2 x 4 = 16
>> x
>>
>> xx : 3 x 1 x 4 = 12
>> x
>> x
>>
>> xxx : 2 x 2 x 2 = 8
>> x
>>
>> x : 3 x 1 x 2 = 6
>> xx
>> x
>>
>> xx : 3 x 2 x 1 = 6
>> xx
>>
>> xx : 2 x 2 x 2 = 8
>> xx
>>
>> x : 3 x 1 x 2 = 6
>> xx
>> x
>>
>> Total: 65
>
> i got 65 too.
>
>
>> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
>>
>> If you're saying you would like a simple formula to get the final number 65, there is not going to
>> be any such 'simple' formula.
>
>
>
> i'd love to see a simple formula for this (or similar) problem.
>
>
> __________________________
>
> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
>
> Assuming that the ans. here is 65...
>
>
> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
>
> ---------- is it bigger or smaller than 6500 ?
>

You can work it out if you like - just adjust all the calculation lines above by upping the h and v
columns appropriately. E.g. for the xxxx line, the new line will be

h v rr Tot

old xxxx : 1 x 3 x 1 = 3
new xxxx : 37 x 30 x 1 = 1110

You have increased the width,height each by a factor of 10. Each such scaling will increase the Tot
column by a factor of (typically) a bit more than 10, so the new answer will be more than 6500.

Considering the number as a fraction of the total number of stamps, the fraction will tend to a
limit as the width/height of the stamp block increases. The limit is determined by adding all the
rr values in the calculation columns, which essentially gives the total number of distinct "shapes"
[*] that can be made out of the connected stamps. Perhaps you're really more interested in the
problem of how many such shapes can be made.

[*] "distinct shapes" means shapes ignoring duplicates resulting from
reflections/rotations/translations.

Mike.

On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
> > On 25/10/2022 17:35, henh...@gmail.com wrote:
> > > On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> > >> On 25/10/2022 05:23, henh...@gmail.com wrote:
> > >>>
> > >>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> > >>>
> > >>>
> > >>>
> > >>> from a 12-square array ( 4 x 3 sheet )
> > >>>
> > >>> How many 2-stamp combinations can you create ?
> > >>> How many 3-stamp combinations can you create ?
> > >>> How many 4-stamp combinations can you create ?
> > >>>
> > >>>
> > >>>
> > >>> Each of the 2,3,4 stamps must be connected by an edge
> > >>>
> > >>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> > >>>
> > >
> > >
> > >> What do you count as separate combinations? Are rotated/translated combinations distinct?
> > >>
> > >> Mike.
> > >
> > >
> > > we can assume that each stamp in the (X times Y) sheet has a different picture.
> > >
> > >
> > > for me ... i'm most curious if there's an answer that comes out simply as
> > > e.g.
> > > (x-1)C(z-1) times (y-1)C(z-1)
> > Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
> >
> > All the answers are like that, but we have to appropriately account for rotations/reflections, and
> > the different shapes that are included in the set to be counted.
> >
> > So... for 4-stamp combinations: (with a 4x3 sheet)
> >
> > h v rr Tot
> >
> > xxxx : 1 x 3 x 1 = 3
> >
> > x : 4 x 0 x 1 = 0
> > x
> > x
> > x
> >
> > xxx : 2 x 2 x 4 = 16
> > x
> >
> > xx : 3 x 1 x 4 = 12
> > x
> > x
> >
> > xxx : 2 x 2 x 2 = 8
> > x
> >
> > x : 3 x 1 x 2 = 6
> > xx
> > x
> >
> > xx : 3 x 2 x 1 = 6
> > xx
> >
> > xx : 2 x 2 x 2 = 8
> > xx
> >
> > x : 3 x 1 x 2 = 6
> > xx
> > x
> >
> > Total: 65
> i got 65 too.
> > [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
> >
> > If you're saying you would like a simple formula to get the final number 65, there is not going to
> > be any such 'simple' formula.
> i'd love to see a simple formula for this (or similar) problem.
>
>
> __________________________
>
> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
>
> Assuming that the ans. here is 65...
>
>
> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
>
> ---------- is it bigger or smaller than 6500 ?

for n x m sheet with n, m >= 3:

xxxx (n-3)*m+(m-3)*n

xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
x

xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
x

xx 2*((n-2)*(m-1)+(n-1)*(m-2))
xx

xx (n-1)*(m-1)
xx

Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)

For 40 x 30 this gives 20,873

Please reply to ilanlmayer at gmail dot com

__/\__
\ /
__/\\ //\__ Ilan Mayer
\ /
/__ __\ Toronto, Canada
/__ __\
||

On Saturday, October 29, 2022 at 9:42:09 AM UTC-4, Ilan Mayer wrote:
> On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
> > On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
> > > On 25/10/2022 17:35, henh...@gmail.com wrote:
> > > > On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> > > >> On 25/10/2022 05:23, henh...@gmail.com wrote:
> > > >>>
> > > >>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> > > >>>
> > > >>>
> > > >>>
> > > >>> from a 12-square array ( 4 x 3 sheet )
> > > >>>
> > > >>> How many 2-stamp combinations can you create ?
> > > >>> How many 3-stamp combinations can you create ?
> > > >>> How many 4-stamp combinations can you create ?
> > > >>>
> > > >>>
> > > >>>
> > > >>> Each of the 2,3,4 stamps must be connected by an edge
> > > >>>
> > > >>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> > > >>>
> > > >
> > > >
> > > >> What do you count as separate combinations? Are rotated/translated combinations distinct?
> > > >>
> > > >> Mike.
> > > >
> > > >
> > > > we can assume that each stamp in the (X times Y) sheet has a different picture.
> > > >
> > > >
> > > > for me ... i'm most curious if there's an answer that comes out simply as
> > > > e.g.
> > > > (x-1)C(z-1) times (y-1)C(z-1)
> > > Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
> > >
> > > All the answers are like that, but we have to appropriately account for rotations/reflections, and
> > > the different shapes that are included in the set to be counted.
> > >
> > > So... for 4-stamp combinations: (with a 4x3 sheet)
> > >
> > > h v rr Tot
> > >
> > > xxxx : 1 x 3 x 1 = 3
> > >
> > > x : 4 x 0 x 1 = 0
> > > x
> > > x
> > > x
> > >
> > > xxx : 2 x 2 x 4 = 16
> > > x
> > >
> > > xx : 3 x 1 x 4 = 12
> > > x
> > > x
> > >
> > > xxx : 2 x 2 x 2 = 8
> > > x
> > >
> > > x : 3 x 1 x 2 = 6
> > > xx
> > > x
> > >
> > > xx : 3 x 2 x 1 = 6
> > > xx
> > >
> > > xx : 2 x 2 x 2 = 8
> > > xx
> > >
> > > x : 3 x 1 x 2 = 6
> > > xx
> > > x
> > >
> > > Total: 65
> > i got 65 too.
> > > [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
> > >
> > > If you're saying you would like a simple formula to get the final number 65, there is not going to
> > > be any such 'simple' formula.
> > i'd love to see a simple formula for this (or similar) problem.
> >
> >
> > __________________________
> >
> > from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
> >
> > Assuming that the ans. here is 65...
> >
> >
> > from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
> >
> > ---------- is it bigger or smaller than 6500 ?
> for n x m sheet with n, m >= 3:
>
> xxxx (n-3)*m+(m-3)*n
>
> xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
> x
>
> xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
> x
>
> xx 2*((n-2)*(m-1)+(n-1)*(m-2))
> xx
>
> xx (n-1)*(m-1)
> xx
>
> Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)
This can be simplified into 19*n*m-28*n-28*m+33

> For 40 x 30 this gives 20,873
>
> Please reply to ilanlmayer at gmail dot com
>
> __/\__
> \ /
> __/\\ //\__ Ilan Mayer
> \ /
> /__ __\ Toronto, Canada
> /__ __\
> ||

On 29/10/2022 18:54, Ilan Mayer wrote:
> On Saturday, October 29, 2022 at 9:42:09 AM UTC-4, Ilan Mayer wrote:
>> On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
>>> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
>>>> On 25/10/2022 17:35, henh...@gmail.com wrote:
>>>>> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
>>>>>> On 25/10/2022 05:23, henh...@gmail.com wrote:
>>>>>>>
>>>>>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> from a 12-square array ( 4 x 3 sheet )
>>>>>>>
>>>>>>> How many 2-stamp combinations can you create ?
>>>>>>> How many 3-stamp combinations can you create ?
>>>>>>> How many 4-stamp combinations can you create ?
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Each of the 2,3,4 stamps must be connected by an edge
>>>>>>>
>>>>>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
>>>>>>>
>>>>>
>>>>>
>>>>>> What do you count as separate combinations? Are rotated/translated combinations distinct?
>>>>>>
>>>>>> Mike.
>>>>>
>>>>>
>>>>> we can assume that each stamp in the (X times Y) sheet has a different picture.
>>>>>
>>>>>
>>>>> for me ... i'm most curious if there's an answer that comes out simply as
>>>>> e.g.
>>>>> (x-1)C(z-1) times (y-1)C(z-1)
>>>> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
>>>>
>>>> All the answers are like that, but we have to appropriately account for rotations/reflections, and
>>>> the different shapes that are included in the set to be counted.
>>>>
>>>> So... for 4-stamp combinations: (with a 4x3 sheet)
>>>>
>>>> h v rr Tot
>>>>
>>>> xxxx : 1 x 3 x 1 = 3
>>>>
>>>> x : 4 x 0 x 1 = 0
>>>> x
>>>> x
>>>> x
>>>>
>>>> xxx : 2 x 2 x 4 = 16
>>>> x
>>>>
>>>> xx : 3 x 1 x 4 = 12
>>>> x
>>>> x
>>>>
>>>> xxx : 2 x 2 x 2 = 8
>>>> x
>>>>
>>>> x : 3 x 1 x 2 = 6
>>>> xx
>>>> x
>>>>
>>>> xx : 3 x 2 x 1 = 6
>>>> xx
>>>>
>>>> xx : 2 x 2 x 2 = 8
>>>> xx
>>>>
>>>> x : 3 x 1 x 2 = 6
>>>> xx
>>>> x
>>>>
>>>> Total: 65
>>> i got 65 too.
>>>> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
>>>>
>>>> If you're saying you would like a simple formula to get the final number 65, there is not going to
>>>> be any such 'simple' formula.
>>> i'd love to see a simple formula for this (or similar) problem.
>>>
>>>
>>> __________________________
>>>
>>> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
>>>
>>> Assuming that the ans. here is 65...
>>>
>>>
>>> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
>>>
>>> ---------- is it bigger or smaller than 6500 ?
>> for n x m sheet with n, m >= 3:
>>
>> xxxx (n-3)*m+(m-3)*n
>>
>> xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
>> x
>>
>> xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
>> x
>>
>> xx 2*((n-2)*(m-1)+(n-1)*(m-2))
>> xx
>>
>> xx (n-1)*(m-1)
>> xx
>>
>> Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)
>
> This can be simplified into 19*n*m-28*n-28*m+33

Right - a 2nd degree polynomial in m,n.

As m,n increase (together), the 19*m*n term dominates, and the result, divided by n*m (number of
stamps) converges to 19.

19 is the number of essentially different shapes we can make with 4 connected stamps.

Mike.

>
>> For 40 x 30 this gives 20,873
>>
>> Please reply to ilanlmayer at gmail dot com
>>
>> __/\__
>> \ /
>> __/\\ //\__ Ilan Mayer
>> \ /
>> /__ __\ Toronto, Canada
>> /__ __\
>> ||

On Saturday, October 29, 2022 at 11:08:48 AM UTC-7, Mike Terry wrote:
> On 29/10/2022 18:54, Ilan Mayer wrote:
> > On Saturday, October 29, 2022 at 9:42:09 AM UTC-4, Ilan Mayer wrote:
> >> On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
> >>> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
> >>>> On 25/10/2022 17:35, henh...@gmail.com wrote:
> >>>>> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> >>>>>> On 25/10/2022 05:23, henh...@gmail.com wrote:
> >>>>>>>
> >>>>>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> from a 12-square array ( 4 x 3 sheet )
> >>>>>>>
> >>>>>>> How many 2-stamp combinations can you create ?
> >>>>>>> How many 3-stamp combinations can you create ?
> >>>>>>> How many 4-stamp combinations can you create ?
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> Each of the 2,3,4 stamps must be connected by an edge
> >>>>>>>
> >>>>>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> >>>>>>>
> >>>>>
> >>>>>
> >>>>>> What do you count as separate combinations? Are rotated/translated combinations distinct?
> >>>>>>
> >>>>>> Mike.
> >>>>>
> >>>>>
> >>>>> we can assume that each stamp in the (X times Y) sheet has a different picture.
> >>>>>
> >>>>>
> >>>>> for me ... i'm most curious if there's an answer that comes out simply as
> >>>>> e.g.
> >>>>> (x-1)C(z-1) times (y-1)C(z-1)
> >>>> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
> >>>>
> >>>> All the answers are like that, but we have to appropriately account for rotations/reflections, and
> >>>> the different shapes that are included in the set to be counted.
> >>>>
> >>>> So... for 4-stamp combinations: (with a 4x3 sheet)
> >>>>
> >>>> h v rr Tot
> >>>>
> >>>> xxxx : 1 x 3 x 1 = 3
> >>>>
> >>>> x : 4 x 0 x 1 = 0
> >>>> x
> >>>> x
> >>>> x
> >>>>
> >>>> xxx : 2 x 2 x 4 = 16
> >>>> x
> >>>>
> >>>> xx : 3 x 1 x 4 = 12
> >>>> x
> >>>> x
> >>>>
> >>>> xxx : 2 x 2 x 2 = 8
> >>>> x
> >>>>
> >>>> x : 3 x 1 x 2 = 6
> >>>> xx
> >>>> x
> >>>>
> >>>> xx : 3 x 2 x 1 = 6
> >>>> xx
> >>>>
> >>>> xx : 2 x 2 x 2 = 8
> >>>> xx
> >>>>
> >>>> x : 3 x 1 x 2 = 6
> >>>> xx
> >>>> x
> >>>>
> >>>> Total: 65
> >>> i got 65 too.
> >>>> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
> >>>>
> >>>> If you're saying you would like a simple formula to get the final number 65, there is not going to
> >>>> be any such 'simple' formula.
> >>> i'd love to see a simple formula for this (or similar) problem.
> >>>
> >>>
> >>> __________________________
> >>>
> >>> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
> >>>
> >>> Assuming that the ans. here is 65...
> >>>
> >>>
> >>> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
> >>>
> >>> ---------- is it bigger or smaller than 6500 ?
> >> for n x m sheet with n, m >= 3:
> >>
> >> xxxx (n-3)*m+(m-3)*n
> >>
> >> xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
> >> x
> >>
> >> xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
> >> x
> >>
> >> xx 2*((n-2)*(m-1)+(n-1)*(m-2))
> >> xx
> >>
> >> xx (n-1)*(m-1)
> >> xx
> >>
> >> Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)
> >
> > This can be simplified into 19*n*m-28*n-28*m+33

so for (40 x 30) sheet... the ans. is 20,873

> Right - a 2nd degree polynomial in m,n.
>
> As m,n increase (together), the 19*m*n term dominates, and the result, divided by n*m (number of
> stamps) converges to 19.
>
> 19 is the number of essentially different shapes we can make with 4 connected stamps. Mike.

i'm counting 18 shapes.... maybe there's a good explanation for why it's 19 (and 28)

On Saturday, October 29, 2022 at 4:19:45 PM UTC-7, henh...@gmail.com wrote:
> On Saturday, October 29, 2022 at 11:08:48 AM UTC-7, Mike Terry wrote:
> > On 29/10/2022 18:54, Ilan Mayer wrote:
> > > On Saturday, October 29, 2022 at 9:42:09 AM UTC-4, Ilan Mayer wrote:
> > >> On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
> > >>> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
> > >>>> On 25/10/2022 17:35, henh...@gmail.com wrote:
> > >>>>> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> > >>>>>> On 25/10/2022 05:23, henh...@gmail.com wrote:
> > >>>>>>>
> > >>>>>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> > >>>>>>>
> > >>>>>>>
> > >>>>>>>
> > >>>>>>> from a 12-square array ( 4 x 3 sheet )
> > >>>>>>>
> > >>>>>>> How many 2-stamp combinations can you create ?
> > >>>>>>> How many 3-stamp combinations can you create ?
> > >>>>>>> How many 4-stamp combinations can you create ?
> > >>>>>>>
> > >>>>>>>
> > >>>>>>>
> > >>>>>>> Each of the 2,3,4 stamps must be connected by an edge
> > >>>>>>>
> > >>>>>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> > >>>>>>>
> > >>>>>
> > >>>>>
> > >>>>>> What do you count as separate combinations? Are rotated/translated combinations distinct?
> > >>>>>>
> > >>>>>> Mike.
> > >>>>>
> > >>>>>
> > >>>>> we can assume that each stamp in the (X times Y) sheet has a different picture.
> > >>>>>
> > >>>>>
> > >>>>> for me ... i'm most curious if there's an answer that comes out simply as
> > >>>>> e.g.
> > >>>>> (x-1)C(z-1) times (y-1)C(z-1)
> > >>>> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
> > >>>>
> > >>>> All the answers are like that, but we have to appropriately account for rotations/reflections, and
> > >>>> the different shapes that are included in the set to be counted.
> > >>>>
> > >>>> So... for 4-stamp combinations: (with a 4x3 sheet)
> > >>>>
> > >>>> h v rr Tot
> > >>>>
> > >>>> xxxx : 1 x 3 x 1 = 3
> > >>>>
> > >>>> x : 4 x 0 x 1 = 0
> > >>>> x
> > >>>> x
> > >>>> x
> > >>>>
> > >>>> xxx : 2 x 2 x 4 = 16
> > >>>> x
> > >>>>
> > >>>> xx : 3 x 1 x 4 = 12
> > >>>> x
> > >>>> x
> > >>>>
> > >>>> xxx : 2 x 2 x 2 = 8
> > >>>> x
> > >>>>
> > >>>> x : 3 x 1 x 2 = 6
> > >>>> xx
> > >>>> x
> > >>>>
> > >>>> xx : 3 x 2 x 1 = 6
> > >>>> xx
> > >>>>
> > >>>> xx : 2 x 2 x 2 = 8
> > >>>> xx
> > >>>>
> > >>>> x : 3 x 1 x 2 = 6
> > >>>> xx
> > >>>> x
> > >>>>
> > >>>> Total: 65
> > >>> i got 65 too.
> > >>>> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
> > >>>>
> > >>>> If you're saying you would like a simple formula to get the final number 65, there is not going to
> > >>>> be any such 'simple' formula.
> > >>> i'd love to see a simple formula for this (or similar) problem.
> > >>>
> > >>>
> > >>> __________________________
> > >>>
> > >>> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
> > >>>
> > >>> Assuming that the ans. here is 65...
> > >>>
> > >>>
> > >>> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
> > >>>
> > >>> ---------- is it bigger or smaller than 6500 ?
> > >> for n x m sheet with n, m >= 3:
> > >>
> > >> xxxx (n-3)*m+(m-3)*n
> > >>
> > >> xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
> > >> x
> > >>
> > >> xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
> > >> x
> > >>
> > >> xx 2*((n-2)*(m-1)+(n-1)*(m-2))
> > >> xx
> > >>
> > >> xx (n-1)*(m-1)
> > >> xx
> > >>
> > >> Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)
> > >
> > > This can be simplified into 19*n*m-28*n-28*m+33
> so for (40 x 30) sheet... the ans. is 20,873
> > Right - a 2nd degree polynomial in m,n.
> >
> > As m,n increase (together), the 19*m*n term dominates, and the result, divided by n*m (number of
> > stamps) converges to 19.
> >
> > 19 is the number of essentially different shapes we can make with 4 connected stamps. Mike.

> i'm counting 18 shapes.... maybe there's a good explanation for why it's 19 (and 28)

> How many 2-stamp combinations can you create ?

2 shapes. CC (Converging Coefficient) is 2

> How many 3-stamp combinations can you create ?

6 shapes.

the CC (Converging Coefficient) must be 6 or 7.

--------------- i'd guess 7.

On 30/10/2022 00:19, henh...@gmail.com wrote:
> On Saturday, October 29, 2022 at 11:08:48 AM UTC-7, Mike Terry wrote:
>> On 29/10/2022 18:54, Ilan Mayer wrote:
>>> On Saturday, October 29, 2022 at 9:42:09 AM UTC-4, Ilan Mayer wrote:
>>>> On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
>>>>> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
>>>>>> On 25/10/2022 17:35, henh...@gmail.com wrote:
>>>>>>> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
>>>>>>>> On 25/10/2022 05:23, henh...@gmail.com wrote:
>>>>>>>>>
>>>>>>>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> from a 12-square array ( 4 x 3 sheet )
>>>>>>>>>
>>>>>>>>> How many 2-stamp combinations can you create ?
>>>>>>>>> How many 3-stamp combinations can you create ?
>>>>>>>>> How many 4-stamp combinations can you create ?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Each of the 2,3,4 stamps must be connected by an edge
>>>>>>>>>
>>>>>>>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
>>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>> What do you count as separate combinations? Are rotated/translated combinations distinct?
>>>>>>>>
>>>>>>>> Mike.
>>>>>>>
>>>>>>>
>>>>>>> we can assume that each stamp in the (X times Y) sheet has a different picture.
>>>>>>>
>>>>>>>
>>>>>>> for me ... i'm most curious if there's an answer that comes out simply as
>>>>>>> e.g.
>>>>>>> (x-1)C(z-1) times (y-1)C(z-1)
>>>>>> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
>>>>>>
>>>>>> All the answers are like that, but we have to appropriately account for rotations/reflections, and
>>>>>> the different shapes that are included in the set to be counted.
>>>>>>
>>>>>> So... for 4-stamp combinations: (with a 4x3 sheet)
>>>>>>
>>>>>> h v rr Tot
>>>>>>
>>>>>> xxxx : 1 x 3 x 1 = 3
>>>>>>
>>>>>> x : 4 x 0 x 1 = 0
>>>>>> x
>>>>>> x
>>>>>> x
>>>>>>
>>>>>> xxx : 2 x 2 x 4 = 16
>>>>>> x
>>>>>>
>>>>>> xx : 3 x 1 x 4 = 12
>>>>>> x
>>>>>> x
>>>>>>
>>>>>> xxx : 2 x 2 x 2 = 8
>>>>>> x
>>>>>>
>>>>>> x : 3 x 1 x 2 = 6
>>>>>> xx
>>>>>> x
>>>>>>
>>>>>> xx : 3 x 2 x 1 = 6
>>>>>> xx
>>>>>>
>>>>>> xx : 2 x 2 x 2 = 8
>>>>>> xx
>>>>>>
>>>>>> x : 3 x 1 x 2 = 6
>>>>>> xx
>>>>>> x
>>>>>>
>>>>>> Total: 65
>>>>> i got 65 too.
>>>>>> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
>>>>>>
>>>>>> If you're saying you would like a simple formula to get the final number 65, there is not going to
>>>>>> be any such 'simple' formula.
>>>>> i'd love to see a simple formula for this (or similar) problem.
>>>>>
>>>>>
>>>>> __________________________
>>>>>
>>>>> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
>>>>>
>>>>> Assuming that the ans. here is 65...
>>>>>
>>>>>
>>>>> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
>>>>>
>>>>> ---------- is it bigger or smaller than 6500 ?
>>>> for n x m sheet with n, m >= 3:
>>>>
>>>> xxxx (n-3)*m+(m-3)*n
>>>>
>>>> xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
>>>> x
>>>>
>>>> xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
>>>> x
>>>>
>>>> xx 2*((n-2)*(m-1)+(n-1)*(m-2))
>>>> xx
>>>>
>>>> xx (n-1)*(m-1)
>>>> xx
>>>>
>>>> Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)
>>>
>>> This can be simplified into 19*n*m-28*n-28*m+33
>
>
> so for (40 x 30) sheet... the ans. is 20,873
>
>
>> Right - a 2nd degree polynomial in m,n.
>>
>> As m,n increase (together), the 19*m*n term dominates, and the result, divided by n*m (number of
>> stamps) converges to 19.
>>
>> 19 is the number of essentially different shapes we can make with 4 connected stamps. Mike.
>
>
> i'm counting 18 shapes.... maybe there's a good explanation for why it's 19 (and 28)

It might be a mistake on my part - 19 comes from counting all the rr column values in my original table.

Here's the table again, but I've added the rotated/reflected shapes

h v rr Tot

--------------------------------
xxxx : 1 x 3 x 1 = 3

--------------------------------
x : 4 x 0 x 1 = 0
x x
x

--------------------------------
xxx : 2 x 2 x 4 = 16
x

x
xxx

xxx
x

x
xxx

--------------------------------
xx : 3 x 1 x 4 = 12
x
x

xx
x x

x
x
xx

x
x xx

--------------------------------
xxx : 2 x 2 x 2 = 8
x

x
xxx

--------------------------------
x : 3 x 1 x 2 = 6
xx
x

x
xx
x

--------------------------------
xx : 3 x 2 x 1 = 6
xx

--------------------------------
xx : 2 x 2 x 2 = 8
xx

xx
xx

--------------------------------
x : 3 x 1 x 2 = 6
xx
x

x
xx
x

So... that's 19 shapes! You must have missed one?

Mike.

On Saturday, October 29, 2022 at 5:46:07 PM UTC-7, Mike Terry wrote:
> On 30/10/2022 00:19, henh...@gmail.com wrote:
> > On Saturday, October 29, 2022 at 11:08:48 AM UTC-7, Mike Terry wrote:
> >> On 29/10/2022 18:54, Ilan Mayer wrote:
> >>> On Saturday, October 29, 2022 at 9:42:09 AM UTC-4, Ilan Mayer wrote:
> >>>> On Friday, October 28, 2022 at 4:19:49 PM UTC-4, henh...@gmail.com wrote:
> >>>>> On Friday, October 28, 2022 at 12:43:33 PM UTC-7, Mike Terry wrote:
> >>>>>> On 25/10/2022 17:35, henh...@gmail.com wrote:
> >>>>>>> On Tuesday, October 25, 2022 at 6:24:10 AM UTC-7, Mike Terry wrote:
> >>>>>>>> On 25/10/2022 05:23, henh...@gmail.com wrote:
> >>>>>>>>>
> >>>>>>>>> ------ pls wait 3+ days (Longer if you find it easy or trivial) before posting answers or hints to the following.
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> from a 12-square array ( 4 x 3 sheet )
> >>>>>>>>>
> >>>>>>>>> How many 2-stamp combinations can you create ?
> >>>>>>>>> How many 3-stamp combinations can you create ?
> >>>>>>>>> How many 4-stamp combinations can you create ?
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> Each of the 2,3,4 stamps must be connected by an edge
> >>>>>>>>>
> >>>>>>>>> for 3-stamp combinations, they'd be horizontal, vertical, or L-shaped
> >>>>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>>> What do you count as separate combinations? Are rotated/translated combinations distinct?
> >>>>>>>>
> >>>>>>>> Mike.
> >>>>>>>
> >>>>>>>
> >>>>>>> we can assume that each stamp in the (X times Y) sheet has a different picture.
> >>>>>>>
> >>>>>>>
> >>>>>>> for me ... i'm most curious if there's an answer that comes out simply as
> >>>>>>> e.g.
> >>>>>>> (x-1)C(z-1) times (y-1)C(z-1)
> >>>>>> Well, if we want a 2x2 square, say, and we have a 4x3 sheet, then we can make 3x2 = 6 such squares.
> >>>>>>
> >>>>>> All the answers are like that, but we have to appropriately account for rotations/reflections, and
> >>>>>> the different shapes that are included in the set to be counted.
> >>>>>>
> >>>>>> So... for 4-stamp combinations: (with a 4x3 sheet)
> >>>>>>
> >>>>>> h v rr Tot
> >>>>>>
> >>>>>> xxxx : 1 x 3 x 1 = 3
> >>>>>>
> >>>>>> x : 4 x 0 x 1 = 0
> >>>>>> x
> >>>>>> x
> >>>>>> x
> >>>>>>
> >>>>>> xxx : 2 x 2 x 4 = 16
> >>>>>> x
> >>>>>>
> >>>>>> xx : 3 x 1 x 4 = 12
> >>>>>> x
> >>>>>> x
> >>>>>>
> >>>>>> xxx : 2 x 2 x 2 = 8
> >>>>>> x
> >>>>>>
> >>>>>> x : 3 x 1 x 2 = 6
> >>>>>> xx
> >>>>>> x
> >>>>>>
> >>>>>> xx : 3 x 2 x 1 = 6
> >>>>>> xx
> >>>>>>
> >>>>>> xx : 2 x 2 x 2 = 8
> >>>>>> xx
> >>>>>>
> >>>>>> x : 3 x 1 x 2 = 6
> >>>>>> xx
> >>>>>> x
> >>>>>>
> >>>>>> Total: 65
> >>>>> i got 65 too.
> >>>>>> [ columns: h = horizontal placements, v = vertical, rr = rotations/reflections ]
> >>>>>>
> >>>>>> If you're saying you would like a simple formula to get the final number 65, there is not going to
> >>>>>> be any such 'simple' formula.
> >>>>> i'd love to see a simple formula for this (or similar) problem.
> >>>>>
> >>>>>
> >>>>> __________________________
> >>>>>
> >>>>> from a 12-square array ( 4 x 3 sheet ) How many 4-stamp combinations can you create ?
> >>>>>
> >>>>> Assuming that the ans. here is 65...
> >>>>>
> >>>>>
> >>>>> from a 1200-square array ( 40 x 30 sheet ) How many 4-stamp combinations can you create ?
> >>>>>
> >>>>> ---------- is it bigger or smaller than 6500 ?
> >>>> for n x m sheet with n, m >= 3:
> >>>>
> >>>> xxxx (n-3)*m+(m-3)*n
> >>>>
> >>>> xxx 4*((n-2)*(m-1)+(n-1)*(m-2))
> >>>> x
> >>>>
> >>>> xxx 2*((n-2)*(m-1)+(n-1)*(m-2))
> >>>> x
> >>>>
> >>>> xx 2*((n-2)*(m-1)+(n-1)*(m-2))
> >>>> xx
> >>>>
> >>>> xx (n-1)*(m-1)
> >>>> xx
> >>>>
> >>>> Total: 8*((n-2)*(m-1)+(n-1)*(m-2))+(n-3)*m+(m-3)*n+(n-1)*(m-1)
> >>>
> >>> This can be simplified into 19*n*m-28*n-28*m+33
> >
> >
> > so for (40 x 30) sheet... the ans. is 20,873
> >
> >
> >> Right - a 2nd degree polynomial in m,n.
> >>
> >> As m,n increase (together), the 19*m*n term dominates, and the result, divided by n*m (number of
> >> stamps) converges to 19.
> >>
> >> 19 is the number of essentially different shapes we can make with 4 connected stamps. Mike.
> >
> >
> > i'm counting 18 shapes.... maybe there's a good explanation for why it's 19 (and 28)
> It might be a mistake on my part - 19 comes from counting all the rr column values in my original table.
>
> Here's the table again, but I've added the rotated/reflected shapes
>
> h v rr Tot
>
> --------------------------------
> xxxx : 1 x 3 x 1 = 3
> --------------------------------
> x : 4 x 0 x 1 = 0
> x
> x
> x
> --------------------------------
> xxx : 2 x 2 x 4 = 16
> x
>
> x
> xxx
>
> xxx
> x
>
> x
> xxx
>
> --------------------------------
> xx : 3 x 1 x 4 = 12
> x
> x
>
> xx
> x
> x
>
> x
> x
> xx
>
> x
> x
> xx
>
> --------------------------------
> xxx : 2 x 2 x 2 = 8
> x
>
> x
> xxx
>
> --------------------------------
> x : 3 x 1 x 2 = 6
> xx
> x
>
> x
> xx
> x
>
> --------------------------------
> xx : 3 x 2 x 1 = 6
> xx
> --------------------------------
> xx : 2 x 2 x 2 = 8
> xx
> xx
> xx
>
> --------------------------------
> x : 3 x 1 x 2 = 6
> xx
> x
>
> x
> xx
> x
>
> So... that's 19 shapes! You must have missed one?
>
>
> Mike.

i'm (was) counting 18 shapes....

i missed the vertical one because it doesn't fit in the original ( 4 x 3 sheet )

henh...@gmail.com presented the following explanation :
> from a 12-square array ( 4 x 3 sheet )
>
> How many 2-stamp combinations can you create ?
> How many 3-stamp combinations can you create ?
> How many 4-stamp combinations can you create ?

78

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Ammammata explained on 02/11/2022 :
> henh...@gmail.com presented the following explanation :
>> from a 12-square array ( 4 x 3 sheet )
>>
>> How many 2-stamp combinations can you create ?
>> How many 3-stamp combinations can you create ?
>> How many 4-stamp combinations can you create ?
>
> 78

ops...

2-stamp 17
3-stamp 22
4-stamp 39

--
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On Wednesday, November 2, 2022 at 7:02:41 AM UTC-7, Ammammata wrote:
> Ammammata explained on 02/11/2022 :
> > henh...@gmail.com presented the following explanation :
> >> from a 12-square array ( 4 x 3 sheet )

i wonder where this convention of (W x H) --- [Width first] comes from

> >> How many 2-stamp combinations can you create ?
> >> How many 3-stamp combinations can you create ?
> >> How many 4-stamp combinations can you create ?
> >
> > 78
> ops...
>
> 2-stamp 17
> 3-stamp 22
> 4-stamp 39

i 'm getting... ( 17, 34, 65 )

one more variation would be... (the rest of the sheet stays in One Piece)

henh...@gmail.com expressed precisely :
>> 2-stamp 17
>> 3-stamp 22
>> 4-stamp 39
>
>
> i 'm getting... ( 17, 34, 65 )

maybe I didn't get the picture :)

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Il giorno Wed 02 Nov 2022 08:08:55p, *henh...@gmail.com* ha inviato su
rec.puzzles il messaggio news:00186d10-c37a-4488-84e9-
94872b24f53dn@googlegroups.com. Vediamo cosa ha scritto:

>> 2-stamp 17
>> 3-stamp 22
>> 4-stamp 39
>
>
> i 'm getting... ( 17, 34, 65 )
>
>

ok, I didn't take as valid those shapes not orthogonally connected,
i.e.

xx
x
x

or

x
xx
x

or

x
xx

etc

--
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