A number puzzle - Math Central

HOME

Math Central

Quandaries & Queries

Question from Gita, a parent:

Ok, we really need help for a homework problem due on Monday morning
I've been trying for 2 hours and can't figure it out---if I can't I'm not sure
how my son can....We've been given a puzzle with the following rules:
--The sum of each side must equal 15
--We can only use the numbers 1,2,3,4,5,6,7, 8
--A number can be used only once
(Hint: Think of all combinations of 3 numbers = 15)
--The puzzle looks like this:

_____ _______ ______

_____ ______

_____ _______ ______

Hi Gita,

If you look at ways of selecting 3 numbers from 1, 2, 3, 4, 5, 6, 7 and 8 you will find that there is only one combination that and contains the number 1 and sums to 15. 1 + 6 + 8 = 15. Thus the combination 1, 6, 8 must be in the solution somewhere since it is the only way to include the number 1.

Since no other 3 number combination contains the 1 and sums to 15, 1 can't be in a corner. Thus you can start with

6	1	8

Now for the sides you need two, 3 number combination that sum to 15, one that contains a 6 and the other contains an 8. Since the sides don't meet these two 3 number combinations can't have any numbers in common.

Can you complete if from here?

If you need more help write back,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.