square mystics

Consider a 3 × 3 square where each small square 1 × 1 is written one of the integers 1,2,3 or square 4.This is called Mystic the sum of the numbers in each row and each column is a multiple of 4. How many squares are mystics?

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

There are 256 3x3 mystic squares, because given the upper-left 2x2 square of a 3x3 mystic square, you can uniquely reconstruct the mystic square, and every 2x2 square is the upper-left 2x2 square of a 3x3 mystic square.

A Former Brilliant Member - 7 years, 9 months ago

Colby, you can explain how to get the answer 256?

Vander Nemitz - 7 years, 9 months ago

The number of 3x3 mystic squares is equal to the number of 2x2 normal squares as per the reasoning above, and there are 256 normal 2x2 squares because you have 4 spots to fill with 4 numbers and 444*4 = 256.

A Former Brilliant Member - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$