Where Do They Belong?

Logic Level 1

$\large \boxed{\phantom0} \: \boxed{\phantom0} \times \boxed{\phantom0} \: \boxed{\phantom0}$

All the digits $1,2,3$ and $4$ are used exactly once to fill in the boxes above to form a product of two 2-digit integers. Maximize this product.

The answer is 1312.

3 solutions

Aaron Tsai
May 13, 2016

$4$ and $3$ are obviously in the tens place of the two numbers.

The closer together the two numbers are, the greater the product, so $41\times32=1312$

Fayssal Abdelli
May 14, 2016

1312 = 41 x 32

Wenjin C.
May 13, 2016

To make the product of the 2 two-digit numbers as large as possible, we have to make the two numbers as close as possible. Since the given digits that we can use are 1, 2, 3, and 4, the highest possible number when the digits can be repeated is 44×44=1936 (since n²>(n–1)(n+1)). But since digits can't be repeated, one of the numbers should have 4 as its tens digit while the other should have the digit 3 in its tens place. Since we should make the 2 numbers as close as possible to attain a greater product, their [absolute] difference must be as small as possible. To get the smallest possible difference, we should put 1 as the units digit of the bigger number of the two and 2 as the units digit of the other; thus attaining 41×32=1312 as the answer to the problem.

Where Do They Belong?

The answer is 1312.

3 solutions

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