Library / /136 of 183

, 2025

Algebra Difficulty 2.5 Junior Find the answer Canada

Each of the digits $7$ , $1$ , $3$ , $6$ , $8$ , and $2$ is placed into one of the squares below
to make an expression containing three 2-digit numbers.

When the first two 2-digit numbers are added and the third is
subtracted, the greatest possible result is

Pick one

Solution

For the greatest possible result, we want the sum of the first
two 2-digit numbers to be as large as possible, and the third 2-digit
number to be as small as possible.

Since the tens digit contributes more to the value of a number than the
ones digit, we choose the two largest digits, $7$ and $8$ , as the tens digits of the first two
2-digit numbers, and the smallest of the given digits, $1$ , as the tens digit of the third 2-digit
number.

Of the remaining digits, $3$ , $6$ , and $2$ , we choose the two largest digits,
$3$ and $6$ , as the ones digits of the first two
2-digit numbers, and $2$ as the ones
digit of the third 2-digit number, which becomes $12$ .

Since $73+86=76+83$ , it does not
matter how we pair the tens digits with the ones digits for the first
two 2-digit numbers.

Thus, the greatest possible result is $73+86-12=147$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

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