Alexei and Boris both have a whole number of chocolates, lollipops and toffees, and the product of the number of each boy's of chocolates, lollipops and toffees is 336. It is known that:

(A) Each boy has fewer chocolates than lollipops.

(B) For each boy, the product of the number of chocolates and lollipops equals the total number of candies he has.

(C) Alexei has more lollipops than toffees.

Determine the number of chocolates, lollipops and toffees possessed by each of Alexei and Boris.

(In reply to re(3): Solution by Richard)

I think for your interpretation, there could be more than one unique solution.  Here's one:

Alexei has 2 chocolates, 8 lollipops, and 6 toffees.

A)  2<8   B) 2*8 = 2+8+6 = 16   C) 8>6

Boris has 3 chocolates, 7 lollipops, and 11 toffees.

A)  3<7   B) 3*7 = 3+7+11 = 21

And, 16 * 21 = 336.

Here's another:

Alexei has 2 chocolates, 6 lollipops, and 4 toffees.

A)  2<6   B) 2*6 = 2+6+4 = 12   C) 6>4

Boris has 4 chocolates, 7 lollipops, and 17 toffees.

A)  4<7   B) 4*7 = 4+7+17 = 28

And 12 * 28 = 336.

There may be more, those are just two I found...

Posted by tomarken on 2006-03-28 17:40:04