
23 Aug 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.
Download this post as PDF (will not include images and mathematical symbols).
Managing Editor of the English Section, Gonit Sora and Research Associate, Cardiff University, UK.
No Comments