Times Four, Reversed

Difficulty ★★☆about 5 minLogic PuzzleDigits and placesMultiples

A four-digit number times 4 gives the number with its digits reversed. What is the original number?

Case Record

Multiply a certain four-digit number by 4, and you get the number with its digits in reverse order. (For example, the reverse of 1234 is 4321.)

Your question

What is the original number?

If you get stuck, open the hints one at a time, in order.

Open hint 1

If times 4 is still four digits, what is the largest the first digit can be?

Open hint 2

If the first digit is odd, the last digit of the product won't work.

Open hint 3

The first digit narrows to 1 or 2.

Your question

What is the original number?

Choose the answer closest to the truth.

2178

The answer is "2178."

2178 × 4 = 8712, which is the reverse.

1089 × 4 = 4356, 1782 × 4 = 7128, and 2718 × 4 = 10872 (five digits). None of them gives the reverse.

Diagram of the solution

Because you try testing four-digit numbers one by one.

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