NMTC Inter Level Problem 4

Probability Level 2

Five points on a circle are numbered 1 , 2 , 3 , 4 , 5 1,2,3,4,5 . A frog jumps in a clockwise direction from one point to another round the circle. If it is on an odd numbered point, it jumps one point, and if it is on an even numbered point, it moves two points. The frog begins at point 5 5 . After 2014 2014 jumps it will be on point

2 4 1 3

Nanayaranaraknas Vahdam by Nanayaranaraknas Vahdam , 22, India

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3 solutions

Utkarsh Grover
Oct 24, 2014

frog will start from 5th point and will go to pt. no. 1 then again it'll jump 1 place to go to 2nd pt. from 2 to 4 then from 4 to 1 then again to 2 and then to 4 . so after first jump it will be on 1. mow we will divide the remaining jumps by 3 as the positions repeat after 3 jumps.diving 2013 by 3 we get the remainder as 0 so the frog would be at point1

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Harry Gross
Oct 15, 2014

The frog will jump onto point 1, then 2, then 4. This cycle repeats. Dividing 2014 by 3 [jumps per cycle] gives a remainder of 1, so 1 jump after the starting point, which is point 1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Anubhav Mahapatra
Sep 17, 2017

After first jump, frog is on 1 After second jump, frog is on 2 After third jump, frog is on 4.....and the cycle of 3 continues Clearly, 2014 leaves a remainder 1 when divided by 3...So after 2014 jumps the frog has moved a net of 1 jump... Answer: 1

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