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2020 Math Kangaroo

Problem 22

Problem 22 · 2020 Math Kangaroo Stretch
Logic & Word Problems sum-constraint

Rita numbered the circles in the figure from 1 to 8, so that the sum of the three numbers on each of the four sides of the square equals 13. What is the sum of the four numbers written on the coloured circles?

Figure for Math Kangaroo 2020 Problem 22
Show answer
Answer: E — 16
Show hints
Hint 1 of 2
Adding the four side-sums counts each corner circle twice.
Still stuck? Show hint 2 →
Hint 2 of 2
Compare that double-count to the total 1+2+...+8.
Show solution
Approach: count corners twice via the side sums
  1. The four sides each total 13, so all four sides together total 4 times 13 = 52.
  2. This sum counts every number once, but the four corner circles twice.
  3. Since 1+2+...+8 = 36, the extra from double-counting the corners is 52 minus 36 = 16.
  4. The colored circles are the corners, so their sum is 16.
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