Please help me solve this problem! I am unable to solve it.

There is a dice.We have to color all the sides of the dice using any number of colors at once out of six colors namely-white,black,yellow,blue,green,red such that no two adjacent sides are of same color.How many ways are there to color the dice?

source:pre-rmo 2014 vijayawada region.

#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 we have to use all the color?

Do you have more RMO problems will you share?

Soumo Mukherjee - 6 years, 8 months ago

No we need not use all the colors at once. Yep, I have many more problems from rmo. I will share them with you in my next posts. Meanwhile you try the above problem.

Venkatkalyan Vadlamudi - 6 years, 8 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}`	$\boxed{123}$