------- pls (pls, Please... PLEASE ! ) wait a few days before posting answers or hints.
------- pls (pls, Please... PLEASE ! ) wait a few days before posting answers or hints.
------- pls (pls, Please... PLEASE ! ) wait a few days before posting answers or hints.

Martin Gardner [ The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications [1 ed.]
(Springer, 1997)

-------------- that is an odd title. Was this the last in the series?

_____________________________________

[ Measuring with Yen ]

This problem was originated by Mitsunobu Matsuyama, a reader in Tokyo. He sent me a supply of Japanese one-yen coins and told me
of the following remarkable facts about them that are not well known
even in Japan.

The one-yen coin is made of pure aluminum, has a
radius of exactly [TWO] centimeter[s], and weighs just one gram.

Thus a supply of yens can be used with a balance scale for determining the
weight of small objects in grams. It also can be used on a plane surface
for measuring distances in centimeters.

It is easy to see how one-yen coins can be placed on a line to
measure distances in even centimeters (two centimeters, four, six, and
so on), but can they also be used to measure odd distances (one, three,
five, and so on)? Show how a supply of one-yen coins can be used for
measuring all integral distances in centimeters along a line.

__________________________

(the Correct size is...)
The Japan Mint started issuing these 1 Japanese Yen coins in 1955. They are currently still in circulation. This Japanese silver-colored 1 yen coin measures 20mm across and weighs 1g.

---------- i wonder how Mr.MG got confused.
ok, (1cm was ) just a typo.

On 8/8/2022 9:05 PM, henh...@gmail.com wrote:
> This problem was originated by Mitsunobu Matsuyama, a reader in Tokyo. He sent me a supply of Japanese one-yen coins and told me
> of the following remarkable facts about them that are not well known
> even in Japan.
>
> The one-yen coin is made of pure aluminum, has a
> radius of exactly [TWO] centimeter[s], and weighs just one gram.
These remarkable facts are also not well known to various numismatic
web sites, such as

https://currencies.fandom.com/wiki/Japanese_1_yen_coin
and
https://en.numista.com/catalogue/pieces1590.html

(When translating from Japanese, or even when measuring in other
languages, take care not to confuse 半径 with 直径 -- nor, for that
matter, with 尺骨.)

(Translations courtesy of https://translate.google.com/ after I'd
formed a suspicion. The coin as described would be *thin*!)

--
esosman@comcast-dot-net.invalid
Look on my code, ye Hackers, and guffaw!

On Monday, August 8, 2022 at 8:20:44 PM UTC-7, Eric Sosman wrote:
> On 8/8/2022 9:05 PM, henh...@gmail.com wrote:
> > This problem was originated by Mitsunobu Matsuyama, a reader in Tokyo. He sent me a supply of Japanese one-yen coins and told me
> > of the following remarkable facts about them that are not well known
> > even in Japan.
> >
> > The one-yen coin is made of pure aluminum, has a
> > radius of exactly [TWO] centimeter[s], and weighs just one gram.
> These remarkable facts are also not well known to various numismatic
> web sites, such as
>
> https://currencies.fandom.com/wiki/Japanese_1_yen_coin
> and
> https://en.numista.com/catalogue/pieces1590.html
>
> (When translating from Japanese, or even when measuring in other
> languages, take care not to confuse 半径 with 直径 -- nor, for that
> matter, with 尺骨.)
>
> (Translations courtesy of https://translate.google.com/ after I'd
> formed a suspicion. The coin as described would be *thin*!)
>
> --
> eso...@comcast-dot-net.invalid > Look on my code, ye Hackers, and guffaw!

thanks.. No typo... just me being careless.

---------- I've been eating alphabet soup. Now I have strong vowel movement.

speaking of coins in Japan ...........

The organization, which has a Japan Post Bank account, was informed of the bank's new system of handling charges for coins in October 2021. It was told that from Jan. 17, 2022, the bank would begin charging handling fees when customers deposit or make payments with coins at bank counters and ATMs.

2019 — In December, Sumitomo Mitsui Banking Corp. started charging customers commissions for deposits of 301 or more coins over the counter.

(Japan Post Bank) The bank charges 550 yen (about $5) for customers dealing with 51 to 100 coins, 825 yen (about $7) for 101 to 500 coins, and 1,100 yen (about ...

On 09/08/2022 4:20 am, Eric Sosman wrote:
> On 8/8/2022 9:05 PM, henh...@gmail.com wrote:
>> This problem was originated by Mitsunobu Matsuyama, a reader in
>> Tokyo. He sent me a supply of Japanese one-yen coins and told me
>> of the following remarkable facts about them that are not well
>> known
>> even in Japan.
>>
>> The one-yen coin is made of pure aluminum, has a
>> radius of exactly  [TWO]  centimeter[s],  and weighs just one
>> gram.
> These remarkable facts are also not well known to various numismatic
> web sites, such as
>
>     https://currencies.fandom.com/wiki/Japanese_1_yen_coin
> and
>     https://en.numista.com/catalogue/pieces1590.html
>
> (When translating from Japanese, or even when measuring in other
> languages, take care not to confuse 半径 with 直径 -- nor, for that
> matter, with 尺骨.)
>
> (Translations courtesy of https://translate.google.com/ after I'd
> formed a suspicion.  The coin as described would be *thin*!)

About 0.3mm.

If we assume "radius of exactly TWO centimetres" should read
"diameter" it comes to 1.17mm or so.

Wikipedia claims 1.5mm.

--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

In article <3cbf42b2-4268-47d8-b905-07f402141175n@googlegroups.com>,
henh...@gmail.com <henhanna@gmail.com> wrote:

>Martin Gardner [ The Last Recreations: Hydras, Eggs, and Other
>Mathematical Mystifications [1 ed.]
>(Springer, 1997)
>
> -------------- that is an odd title. Was this the
>last in the series?

Yes. There have been various editions of collections of his
Scientific American columns, and there is now a set of 15, of which
this is the last.

-- Richard

On 8/8/2022 6:05 PM, henh...@gmail.com wrote:

> The one-yen coin is made of pure aluminum, has a
> radius of exactly [TWO] centimeter[s], and weighs just one gram.
>
> Thus a supply of yens can be used with a balance scale for determining the
> weight of small objects in grams. It also can be used on a plane surface
> for measuring distances in centimeters.
>
> It is easy to see how one-yen coins can be placed on a line to
> measure distances in even centimeters (two centimeters, four, six, and
> so on), but can they also be used to measure odd distances (one, three,
> five, and so on)? Show how a supply of one-yen coins can be used for
> measuring all integral distances in centimeters along a line.

[spoiler space]

Find the center of one face:

https://www.instructables.com/How-to-find-the-center-of-a-circle/

If "radius" was a thinko for "diameter", then this is sufficient to
produce a distance of 1 centimeter. If not, then find the midpoint
between the center and any point on the surface.

On Sunday, August 14, 2022 at 9:18:44 PM UTC-4, Edward Murphy wrote:
> On 8/8/2022 6:05 PM, henh...@gmail.com wrote:
>
> > The one-yen coin is made of pure aluminum, has a
> > radius of exactly [TWO] centimeter[s], and weighs just one gram.
> >
> > Thus a supply of yens can be used with a balance scale for determining the
> > weight of small objects in grams. It also can be used on a plane surface
> > for measuring distances in centimeters.
> >
> > It is easy to see how one-yen coins can be placed on a line to
> > measure distances in even centimeters (two centimeters, four, six, and
> > so on), but can they also be used to measure odd distances (one, three,
> > five, and so on)? Show how a supply of one-yen coins can be used for
> > measuring all integral distances in centimeters along a line.
> [spoiler space]
>
> Find the center of one face:
>
> https://www.instructables.com/How-to-find-the-center-of-a-circle/
>
> If "radius" was a thinko for "diameter", then this is sufficient to
> produce a distance of 1 centimeter. If not, then find the midpoint
> between the center and any point on the surface.

If you build a hexagonal tiling of circles, they provide alternating columns
offset by the radius. So, just using two columns will do.

L. Flynn

Jp 5-yen coin has a hole in the middle.

>
> Martin Gardner [ The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications [1 ed.]
> (Springer, 1997)
>

>
> [ Measuring with Yen ]
>
> This problem was originated by Mitsunobu Matsuyama, a reader in Tokyo. He sent me a supply of Japanese one-yen coins and told me
> of the following remarkable facts about them that are not well known
> even in Japan.
>
> The one-yen coin is made of pure aluminum, has a
> radius of exactly one centimeter, and weighs just one gram.
>
> Thus a supply of yens can be used with a balance scale for determining the
> weight of small objects in grams. It also can be used on a plane surface
> for measuring distances in centimeters.
>

i've never been able to figure out if [... is originated by ...]
is a common phrasing or it's really awkward and uncommon.

(maybe it's pretty common in Business and Science )

>>> Our approach to endogenous productivity growth was originated by Jorgenson and Fraumeni ( 1981 ) . The implementation of a general equilibrium model of production that incorporates both substitution among inputs and endogenous ...