Table 100

Is it possible to write either a 0, a 1 or a 2 into each cell of a $100\times 100$ square, such that the sum of the 100 numbers in each row and column is different?

#Combinatorics

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

Do you mean that the sum of the numbers in a row is different to all the other sums of rows and not columns? In other words, can a row and column have the same sum?

If you want no row or column to have the same sum as any other row or column, this makes it easier, as there are 201 possible sums, and 200 possible rows/columns.

Stephen Mellor - 3 years, 5 months ago

we can have sums 0 ~ 200, so that means we have 201 sums. We have 100 rows and 100 columns, which means we have 200 rows and columns. This means we have 200 ways to do this.

Sub to Pewdiepie - 2 years, 2 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}`	$\boxed{123}$