**A** simple riddle from The Riddler on choosing between the maximum between two minima of two throws of an N-face dice, the minimum between two maxima of two throws of an N-face dice, and a single throw. Since maximin is always less than minimax, second choice is always worse than first and a stochastic domination version of the argument shows the single throw should stand in the middle.

## Archive for dice

## minimax, maximin or plain

Posted in Kids, R with tags dice, minimax problem, stochastic dominance, The Riddler on June 1, 2020 by xi'an## Le Monde puzzle [#847]

Posted in Books, Kids, R, Statistics with tags dice, gamma distribution, Le Monde, mathematical puzzle on December 29, 2013 by xi'an**A**nother X’mas Le Monde mathematical puzzle:

A regular dice takes the values 4, 8 and 2 on three adjacent faces. Summit values are defined by the product of the three connected faces, e.g., 64 for the above. What values do the three other faces take if the sum of the eight summit values is 1768?

**H**ere is the simple R code I used to find a solution:

summi=function(x){ #(x[1],x[2],x[3]) opposed to (4,8,2) sum(outer(c(2,x[1]),outer(c(8,x[2]),c(4,x[3]),"*"),"*"))} faces=matrix(sample(1:20,3*10^4,rep=T),ncol=3) resum=apply(faces,1,summi) sol=faces[resum==1768,]

with the result:

> sol [,1] [,2] [,3] [1,] 2 18 13 [2,] 2 18 13 [3,] 2 18 13 [4,] 6 5 13

which means the missing faces are (6,5,13) since the puzzle also imposed all faces were different. The following histogram of the sample of sums shows a reasonable gamma G(1.9,1763) fit.