another viral math puzzle

May 24, 2015

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

After the Singapore Maths Olympiad birthday problem that went viral, here is a Vietnamese primary school puzzle that made the frontline in The Guardian. The question is: Fill the empty slots with all integers from 1 to 9 for the equality to hold. In other words, find a,b,c,d,e,f,g,h,i such that


With presumably the operation ordering corresponding to


although this is not specified in the question. Which amounts to


and implies that c divides b and i divides gxh. Rather than pursing this analytical quest further, I resorted to R coding, checking by brute force whether or not a given sequence was working.

if (ord[1]+(13*ord[2]/ord[3])+ord[4]+
ord[9])-10==66) return(ord)}

I then applied this function to all permutations of {1,…,9} [with the help of the perm(combinat) R function] and found the 128 distinct solutions. Including some for which b:c is not an integer. (Not of this obviously gives a hint as to how a 8-year old could solve the puzzle.)

Filed under: Books, Kids, R, University life Tagged: mathematical puzzle, permutation, primary school, The Guardian, Vietnam

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