multiplying the bars

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The latest Riddler makes the remark that the expression


has no unique meaning (and hence value) since it could be

| -1x|-2|-3 | = 5   or   |-1| – 2x|-3| = -5

depending on the position of the multiplication sign and asks for all the possible values of


which can be explored by a recursive R function for computing |-i|-(i+1)|…|-(i+2j)|

  if(j>1){for(k in 1:(j-2))

producing 40 different values for the ill-defined expression. However, this is incorrect as the product(s) hidden in the expression only involve a single term in vol(i,j)… I had another try with the decomposition of the expression vol(i,j) into a first part and a second part

prod<-function(a,b) a*b[,1]+b[,2]

    if(j-1){for(k in 2:(j-1)){
      for(m in 1:dim(pon)[1])

but it still fails to produce the right version.

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