Can you find a five-digit number that...
...if you place a 9 at the beginning is four times larger than if you place a 9 at the end instead?
Puzzle Copyright © Kevin Stone
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Hint
What's a mathematical way to describe placing a 9 at the beginning?
Answer
23,076.
Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (e.g. 12,345 + 900,000 becomes 912,345).
Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (e.g. 12,345 x 10 + 9 becomes 123,459).
Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:
k + 900,000 = 4 x (10k + 9)
k + 900,000 = 40k + 36
900,000 - 36 = 40k - k
899,964 = 39k
899,964 ÷ 39 = k
Therefore k = 23,076.
Double-Checking
923,076 = 4 x 230,769. This confirms the answer.
