Problem 22 · 2014 Math Kangaroo
Stretch
Number Theory
cryptarithmplace-value
In each box exactly one of the digits 0, 1, 2, 3, 4, 5 and 6 is to be written. Each digit is used only once. The picture on the right shows two 2-digit numbers being added to give a 3-digit number. Which digit has to be written in the grey box so that the sum is correct?
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Answer: D — 5
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Hint 1 of 3
The answer has 3 digits, so the two 2-digit numbers must add up to at least 100.
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Hint 2 of 3
You only have the digits 0 to 6 once each, so the hundreds digit of the answer can only be 1.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you know the answer starts with 1, fit the remaining digits and read the grey (ones) box.
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Approach: find the only valid sum, then read the grey (units) box
- Two 2-digit numbers add to a 3-digit number using 0..6 once each.
- The only working sum is 105 (e.g. 42 + 63), using digits 0,1,2,3,4,5,6.
- The grey box is the units digit of the result, which is 5.
- Answer: 5.
Mark:
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