Question

Create two groups of cards with the same sum using 7,3,1,2,8,6

Answer 1

We must create two groups of cards with the same sum using the following numbers:

`1,2,3,6,7,8`

Summing all the numbers we get:

`1+2+3+6+7+8=27`

We see that the result of the sum is an odd number, that's because we have an odd number of odd numbers. If we split the set of numbers into two groups, we won't be able to put the same number of odd numbers in each group, as result we will have:

• one group whose sum is equal to an even number,

,

• a second group whose sum is equal to an odd number.

So we see that by splitting the set of numbers {1,2,3,6,7,8}, is impossible to get two sets of numbers with the same sum.

If we don't use all the numbers in the set, we can form the following groups of cards with the same sum:

• A = {1,8}, B = {2,7}, the sum of the cards in each group is equal to 9.

,

• A = {2,8}, B = {3,7}, the sum of the cards in each group is equal to 10.