A Reader's Solution

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A Reader's Solution

September 1999

The first correct solution we received for Puzzle No 8 - The Gobbling Goat was this one from V. Shashidhar.

You can see the more detailed PASS Maths solution for a step-by-step explanation of how to tackle the problem.


The answer to the question is 115.8 metres.

Solution diagram 1

It comes as a root to the equation 2r2arcsin(L2r)L24r2L2+L2arccos(L2r)=πr22 where r=100 metres and L is the length of the rope used to tie the goat. \par The derivation is as follows (see figure): θ=2arccosL2rϕ=4arcsinL2rArea(CDEB)=θL22Area(DCF)=Area(ADFC)Area(ADC)=r2arcsinL2rL44r2L2Area(EDFCGB)=Area(CDEB)+2Area(DCF)=πr22 This implies equation (1).