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Problem 357

Algebra Difficulty 2.4 Find the answer CEMC Fermat

The numbers $5,6,10,17$ , and 21 are rearranged so that the sum of the first three numbers is equal to the sum of the last three numbers. Which number is in the middle of this rearrangement?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

When a list of 5 numbers $a, b, c, d, e$ has the property that $a+b+c=c+d+e$ , it is also true that $a+b=d+e$ . With the given list of 5 numbers, it is likely easier to find two pairs with no overlap and with equal sum than to find two triples with one overlap and equal sum. After some trial and error, we can see that $6+21=10+17$ , and so the list $6,21,5,10,17$ has the given property, which means that 5 is in the middle.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.