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Just Keep the Change (Posted on 2003-06-15) Difficulty: 3 of 5
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?

  Submitted by DJ    
Rating: 4.1818 (11 votes)
Solution: (Hide)
2¢ and 5¢

To make 13¢ and odd number, you need an odd number of odd coins. One 5¢ piece accomplishes this, and four two-cent pieces are needed to make up the other eight cents.
To make 14¢, however, you can use two five-cent pieces for ten cents, and two two pence to make fourteen.

Also, these must be the only two denominations of coin worth less than fifteen cents. Any coin with an odd value would mean requiring fewer steps to make 13; any coin with an odd value would require fewer steps to make fourteen.

So, the complete set of coins in this country, worth less than 15¢, are 2¢ and 5¢.

As to the bonus, the country is one I made up. It's called Deejopia, and coins come in values of 2¢, 5¢, 20¢, and 35¢.

Actually, I just didn't want to lack an answer. I don't know of any [real] country in which the only coins worth less than 15¢ are two- and five-cent pieces. Sorry to be misleading, but it seemed a fun question to ask, at least.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Alternate solution and thoughtsJer2016-03-24 13:38:53
SolutionSolutionMath Man2014-07-12 11:32:24
SolutionWithout a country...Dej Mar2012-04-25 04:15:31
re(3): CountryTomM2003-06-16 19:50:28
re: Maybe...TomM2003-06-16 18:12:58
Some ThoughtsMaybe...Pickels2003-06-16 16:05:34
re(3): CountryTrevor Leitch2003-06-16 12:45:35
re(2): CountryJonny Doe2003-06-16 10:19:32
re: Countryfwaff2003-06-16 03:40:53
SolutionCountryJonny Doe2003-06-16 03:35:45
SolutionSolutionTrevor Leitch2003-06-15 09:59:11
Hints/Tipsre: One PossibilityDJ2003-06-15 07:03:32
SolutionOne PossibilityCharlie2003-06-15 05:42:52
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