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Algebra Difficulty 2.4 Junior Find the answer Canada

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?

Pick one

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.

(We note that these two pairs are the only such pairs, after allowing
for switching the numbers in each pair and/or switching the pairs.)

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.