The Flower Puzzle Generalized

 

This article is a crazy generalization of the Flower puzzle by Ankush Goswami published in Gonit Sora on 12th July 2012. We now suppose that instead of three there are m temples A_{1}, A_{2},dots ,A_{m } and instead of doubling, the flowers increase n times in number instantly. Let the priest come to the temple with x flowers and keep y flowers in each temple. So after keeping y flowers in temple A_{1} the priest has nx-y flowers which instantly become n^{2}x-ny ; after keeping in temple A_{2} number of flowers become n^{3}x-n^{2}y-ny and so after keeping in the m th temple number of flowers become n^{(m+1)}x-n^{m}y-n^{(m-1)}y-dots -ny which should actually be equal to zero !! Thus

n^{(m+1)}x-n^{m}y-n^{(m-1)}y-dots -ny =0

Rightarrow frac{x}{y}=frac{1+n+n^2+n^3+dots +n^{m-1}}{n^m}

Rightarrow frac{x}{y}=frac{n^m-1}{n^m(n-1)}

The above relation gives all possible values of the number of flowers brought by the priest (x) and the number of flowers given by him in each temple (y) .

 

Debashish Sharma, JRF, Dept of Mathematics, NIT Silchar.

 

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