Problem 12 · 2018 Math Kangaroo
Medium
Arithmetic & Operations
work-backward
The four smudges hide four of the numbers 1, 2, 3, 4, 5. The calculations along the two arrows are both correct. Which number is hidden behind the smudge with the star?
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Answer: E — 5
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Hint 1 of 2
Each smudge hides one of 1, 2, 3, 4, 5; test which assignment makes both arrow-chains land on 8.
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Hint 2 of 2
Work the multiply/divide arrow first, since those choices are tight, then check the add/subtract arrow.
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Approach: try the few possibilities so both chains give 8
- The four smudges hide four of the numbers 1, 2, 3, 4, 5, and each arrow's calculation must equal 8.
- Only one way to place the numbers makes both the + / - path and the x / div path come out to 8.
- In that solution the star smudge is 5.
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