Problem 29 · 2025 Math Kangaroo
Stretch
Algebra & Patterns
work-backwardsubstitution
The number 8 and another number x are written on a board. Eight children go to the board, one after the other. Each child writes down the average of all the numbers already on the board. The last child writes the number 26. What is the value of x?
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Answer: D — 44
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Hint 1 of 2
Each child writes the average of everything on the board so far, then that value joins the board.
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Hint 2 of 2
Adding a number equal to the current average leaves the average unchanged — so every entry equals the average of 8 and x.
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Approach: the running average never changes
- After the first two numbers, the average is (8+x)/2; writing that value keeps the average the same.
- Hence every child writes exactly (8+x)/2, including the last who wrote 26.
- So (8+x)/2 = 26 → x = 44.
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