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A Three-Digit Number

Solution Step 0/0
I am thinking of a three-digit number. If you subtract 7 from it, the result is divisible by 7; if 8, divisible by 8; and if 9, divisible by 9.

What is the number?

Explanations

Based on the nature of the given subtractions, even without them, it can be seen the original number is divisible by 7, 8, and 9 respectively. The lowest common multiple (LCM) of 7, 8, and 9 is 504. This is the answer, since any further multiples of it (x7, x8, x9) all have at least 4 digits.

[After Boris A. Kordemsky. The Moscow Puzzles: 359 mathematical recreations. 1972]
Check 504
Check 534
Check 564
Check 594

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    • Puzzle A Three-Digit Number

    Puzzle A Three-Digit Number