Problem 11 · 2021 Math Kangaroo
Medium
Number Theory
place-value
The number 5021972970 is written on a sheet of paper. Julian cuts the sheet twice, so he gets 3 numbers. What is the smallest sum he can get by adding these 3 numbers?
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Answer: B — 3444
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Hint 1 of 2
Two cuts give three numbers; their sum is smallest when fewer digits sit in high place-value spots.
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Hint 2 of 2
Avoid leaving any single long piece with a large leading digit — spread the digits so the place values stay low.
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Approach: place the cuts to minimise total place value
- The string is 5021972970; two cuts split it into three numbers.
- Cutting as 502 | 1972 | 970 keeps the high place values small.
- Their sum is 502 + 1972 + 970 = 3444, the smallest achievable.
Mark:
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