Problem 16 · 2017 Math Kangaroo
Medium
Algebra & Patterns
sum-constraintsubstitution
Ria wants to write a number into each box. She has already written two numbers. The sum of all five numbers should be 35, the sum of the first three numbers should be 22, and the sum of the last three numbers should be 25. What is the product Ria gets if she multiplies the two numbers in the grey boxes?
Show answer
Answer: A — 63
Show hints
Hint 1 of 2
The full sum minus the first three minus the last three double-counts only the middle box.
Still stuck? Show hint 2 →
Hint 2 of 2
Use the running sums to pin down each grey box.
Show solution
Approach: solve the box values from overlapping sums
- first3 + last3 = 22 + 25 = 47 = total (35) + middle, so the middle box = 12.
- First three: 3 + grey1 + 12 = 22, so grey1 = 7. Last three: 12 + grey2 + 4 = 25, so grey2 = 9.
- Product of grey boxes = 7 × 9 = 63.
Mark:
· log in to save