# another viral math puzzle

May 24, 2015
By

(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

a+13xb:c+d+12xef-11+gxh:i-10=66.

With presumably the operation ordering corresponding to

a+(13xb:c)+d+(12xe)f-11+(gxh:i)-10=66

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

a+(13xb:c)+d+(12xe)f+(gxh:i)=87

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.

```baoloc=function(ord=sample(1:9)){
if (ord+(13*ord/ord)+ord+
12*ord-ord-11+(ord*ord/
ord)-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  To leave a comment for the author, please follow the link and comment on their blog: Xi'an's Og » R.

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