Jumping Jack

Number Theory Level 3

A frog is sitting on the origin of the coordinate plane. It can jump a distance of five units to points with integer coordinates only (also known as lattice points). Find the least number of jumps required to go to ( 0 , 1 ) . (0,1).

5 4 2 3

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Soumava Pal by Soumava Pal , 22, India

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3 solutions

Ramesh Goenka
Oct 2, 2014

The another possible route is (-4,3) => (0,6) => (0,1) . i guess there has to be finite number of paths through which one can reach to (0,1) ... ! the question is how many paths ??

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Rajen Kapur
Oct 2, 2014

The grid points 5 units apart are in the sequence: (0,0) to (0,-5) to (4,-2) to (0,1) in 3 steps. Answer = 3

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Wait, how about....

(0, 0) => (-3, 4i) => (0, i)?

(0, 0) => (-3, 4i) is 3 units left, 4 units up. (Solving for the absolute value, or the distance from these two points is 5.)

(-3, 4i) => (0, i) is 4 units right, 3 units down. (Again, the absolute value is 5.)

Why not two?

Joeie Christian Santana - 6 years, 8 months ago

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Because my friend, 4 units right and 3 units down is (1 + i), not (0 + i)

Timothy Amado - 6 years, 8 months ago

question is more of logical type..... since it jumps 5 units ..

1st step -> to move farther from the point

2nd step->to go to a point which is 5 units away from (0,1)

3rd step->tada...(0,1) reached..

one might ask why not 2.....cuz its obvious that with 2 steps the nearest point to (0,1)at which we can reach is origin itself... jzt jump to a point and come back

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