Sum Equals Product

Difficulty ★☆☆about 5 minLogic PuzzleTrial and errorIntegers

Three different positive integers whose sum equals their product?

Case Record

There is a combination of three different positive integers whose sum equals their product.

Your question

Which three numbers are they?

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

Open hint 1

Try from the small numbers in order.

Open hint 2

If 1 is included, the product stays small.

Open hint 3

Compare the difference between the product and the sum.

Your question

Which three numbers are they?

Choose the answer closest to the truth.

1, 2, 3

The answer is "1, 2, 3."

1 + 2 + 3 = 6 and 1 × 2 × 3 = 6, so the sum and product are equal.

1, 2, 4 has sum 7 and product 8; 1, 3, 4 has sum 8 and product 12; 2, 3, 4 has sum 9 and product 24. None are equal.

Diagram of the solution

Because the bigger the numbers, the further the product pulls away from the sum.

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