Problem 19 · 2015 Math Kangaroo
Medium
Counting & Probability
careful-countingcasework
How many three-digit positive whole numbers are there, where the digits when placed side by side always differ by 3?
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Answer: D — 20
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Hint 1 of 2
Pick the first digit (1–9), then each later digit must be exactly 3 more or 3 less.
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Hint 2 of 2
Build the number digit by digit, branching by ±3 and discarding any digit outside 0–9.
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Approach: branch by ±3 from each digit
- The hundreds digit is 1–9; each next digit differs from the previous by exactly 3 (so 0–9).
- Carefully listing the valid chains (e.g. 141, 147, 252, 258, 303, ...) gives 20 numbers.
- Count = 20.
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