Threaded Pins aro A number of pins then looped round a third pin is the same as

Question

Threaded Pins aro A number of pins then looped round a third pin is the same as t illustrated in the example. s are placed around a circle. A thread is tied to one pin, and tightly around a second pin. The thread is then looped tightly pin so that the clockwise gap between the first and second he clockwise gap between the second and third pin as 3 pins, gap of 1 5 pins, gap of 2 6 pins, gap of 3 The process is continued, always preserving the same clockwise gap until the first pin is reached. If some pin has not yet been used, the process starts again. Five pins with a gap of two use just one thread, while six pins with a gap of three use three threads. How many pieces of thread will be needed in general?

Explanation / Answer

Here

the number of pieces of thread will be needed is the

greatest common divisor of number of pins and the gap

eg: gcd ( 3 , 1 ) = 1

gcd(5,2) = 1

gcd(6,3) = 3

Here we can take gap as the step size that is if it is 2 then we move from 1 to 3 or 2 to 4

and thread can be taken as cycle

suppose for 6- pins it will {1,2,3,4,5,6}

i.e

for 6 pin and gap 3

it will be into 3 splits i.e 1,4 ; 2,5 ; 3.6

so finally the number of pieces needed will be gcd of number of pins and gap

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