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(2): Solution by tomarken)

Bravo, tomarken!

I came to the same solution as you --(though I had a disadvantange due to a headache I received from a little skull-stepping). :-)

Alexia: 2 chocolates, 12 toffies, 14 lollipops
2  * 14  * 12  = 336
[A]  2 (chocolates) < 14 (lollipops)
[B]  2 (chocolates) + 14 (lollipops) + 12 (toffies) = 28 (candies)
      2 (chocolates) * 14 (lollipops)  = 28
[C] 14 (lollipops) > 12 (toffies)

Boris: 4 chocolates, 6 lollipops, 14 toffies
4 * 6 * 14 = 336
[A]  4 (chocolates) < 6 (lollipops)   
[B]  4 (chocolates) + 6 (lollipops) + 14 (toffies) = 24 (candies)
       4 (chocolates) * 6 (lollipops)  = 24 
   

Edited on March 28, 2006, 5:37 pm

Posted by Dej Mar on 2006-03-28 17:22:20