UCD Openday 2003
Mathematics Problem
You must follow the rules.
CYCLIC-CHANCE
The faces of three dice A,B and C are to be numbered from 1 to 18.
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Find a way to do this so that in a toss of two dice
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on average A will beat B and
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on average B will beat C and
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on average C will beat A.
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Compute the probability P of winning a game of Dicey Reilly
(see below) when using the three dice A,B,C you designed in (i).
Note
The entrant with highest value for P wins first prize.
Dicey Reilly
Play as follows
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Your unsuspecting opponent is allowed first choice of the three dice
A,B,C.
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From the remaining two dice you choose that die which will
on average beat your opponent's die.
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Put aside the remaining die.
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Toss the two chosen dice.
terminology:-
When two dice, say A and B are tossed
the die with the highter score wins. By
A beats B on average we mean that
A is more likely than B to win in such a toss.
Page maintained by
jbquig@ucd.ie
Revised 10 Mar 2003.