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 (for example 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example 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

**9**23,076 = 4 x 230,76**9**. This confirms the answer.