Solution to the Problem:
You have eaten one white mint.
You know that there are twice as many gumdrops as yellow candies and twice as many jellybeans as blue candies.
This can be expressed as the following equation:
(gumdrops + jellybeans) = 2 x (yellow candies + blue candies)
Since you know that the total number of yellow and blue gumdrops and yellow and blue jellybeans is 9, you can rewrite the equation as follows:
(white gumdrops + white jellybeans + 9) = 2 x (yellow mints + blue mints + 9)
You also know that there are twice as many white candies as mints:
(white gumdrops + white jellybeans + white mints) = 2 x (yellow mints + blue mints + white mints)
Examination of the last two equations shows that they are identical except that "white mints" has replaced"9."
Therefore, nine white mints remain, so you have eaten one.
Note: the solution does not determine the distribution of the other candies.
Here's one possible set of remaining candies:
Mints: 9 white, 1 blue, 1 yellow
Gumdrops: 7 white, 2 blue, 5 yellow
Jellybeans: 6 white, 1 blue, 1 yellow
Click here for Sreeroopa Sankararaman's excellent solution
James Alarie wrote:
Whew! I wrote a Perl program to search all one BILLION (!)
possibilities and found 1504 solutions. In every single one, there
were nine white mints remaining. This means that there was exactly 1
mint eaten for all 1504 solutions. I'll be nice and only quote the
first one that I found:
0 yellow gumdrops
0 blue gumdrops
0 white gumdrops
0 yellow jellybeans
9 blue jellybeans
9 white jellybeans
0 yellow mints
0 blue mints
9 white mints
0 total gumdrops
18 total jellybeans
9 total mints
0 total yellow
9 total blue
18 total white