Mathematic-Online problems: Interactive Problem 22: Different dice

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	Mathematics-Online problems:
	Interactive Problem 22: Different dice

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#./interaufg22_en.tex#On a die the numbers 1 to 6 are depicted by the common symbols. Two dice are considered equal, if they can be rotated in space in such a way that corresponding faces show the same symbol in the same arrangement. Accordingly, the dice shown below are thus all different.

$\includegraphics{wuerfel}$

How many different dice are possible, if the spots on opposite faces add up to seven, as is commonly demanded?
How many different dice are possible, if there is no such restriction?
How many different dice are possible, if it is demanded that there is at least one pair of opposite faces whose spots add up to nine?

Answer:

Number of different dice, if

$\bullet$ opposite faces add up to 7 spots

$\bullet$ opposite faces add up to any number of spots

$\bullet$ at least one pair of opposite faces adds up to 9 spots

(From: Day of Mathematics 1992)

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automatically generated: 2/ 6/2018

Number of different dice, if
$\bullet$	opposite faces add up to 7 spots
$\bullet$	opposite faces add up to any number of spots
$\bullet$	at least one pair of opposite faces adds up to 9 spots