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 Just Keep the Change (Posted on 2003-06-15)
In a certain country, it takes a minimum of exactly 5 coins to make 13 cents, and a minimum of exactly 4 coins to make 14 cents.

What are the denominations of the coins (of value less than 15 cents) in this country?

Bonus: What country is it?

 See The Solution Submitted by DJ Rating: 4.1818 (11 votes)

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 Without a country... | Comment 11 of 13 |
Coin denominations have been officially minted in various values. Those values that have been minted in cents under 15¢ are: ¼¢, ½¢, 1¢, 2¢, 2½¢, 3¢, 5¢, and 10¢

Given the possibility of any combination of these there are two possible solutions to the coin denominations:
2¢ and 5¢
13¢ = 2¢+2¢+2¢+2¢+5¢
14¢ = 2¢+2¢+5¢+5¢
and
¼¢, 2¢, 2½¢, and 5¢
13¢ = ¼¢+¼¢+2½¢+5¢+5¢ OR 2¢+2¢+2¢+2¢+5¢
14¢ = 2¢+2¢+5¢+5¢

There is not a nation that is limited to only these denominations for cent coins under 15¢. In addition to these I've listed, cent coins have also been minted for 15¢, 20¢, 25¢, 50¢, 100¢ and 250¢.
One should note that coins identified as cents are not to be confused with coins designated as half-penny, penny, dime, quarter dollar, half dollar, and dollar coins, etc. Though these coins may be identified equivalent to coins valued in cents (as they are subunits or a multiple of subunits of the decimilized base unit where 1 cent = 1/100 of the base unit, usually the dollar), they are not strictly cents, as a cent is the name of the subunit just as the piaster and pence are both 1/100 subunits of a pound (for different national currencies).

Edited on April 25, 2012, 4:49 pm
 Posted by Dej Mar on 2012-04-25 04:15:31

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