Thread: Five points on a circle...

1. Five points on a circle...

Five points on a circle are number 1, 2, 3, 4, and 5 in clockwise order. A bug jumps in a counterclockwise direction from one point to another around the circle. If it is an odd numbered point, it moves two points, and if it on an evn number point, it moves on point. If the bug begins on point 1, what point will it be on after 2007 jumps?

2. Originally Posted by ceasar_19134
Five points on a circle are number 1, 2, 3, 4, and 5 in clockwise order. A bug jumps in a counterclockwise direction from one point to another around the circle. If it is an odd numbered point, it moves two points, and if it on an evn number point, it moves on point. If the bug begins on point 1, what point will it be on after 2007 jumps?
ok, so i don't recall any "method" to do this problem, so if someone has a method, please post it. i attempted to use common sense (which i don't do often) so let's see what happens.

if the bug starts at 1, it will jump counter clockwise 2 spaces and end up at 4, since 4 is even, it jumps once to 3, then since 3 is odd, it jumps 2 spaces to one. and then the same process repeats. 1 4 3 1 4 3 1 4 3 1 ....

the bug takes 3 jumps to complete one cycle, that is, after 3 jumps, it is back on point 1 and start over. now, 2007 is divisible by 3. 2007/3 = 669. so the bug will complete exactly 669 cycles after 2007 jumps, and therefore it will be back to point 1 on it's 2007th jump

3. Originally Posted by ceasar_19134
Five points on a circle are number 1, 2, 3, 4, and 5 in clockwise order. A bug jumps in a counterclockwise direction from one point to another around the circle. If it is an odd numbered point, it moves two points, and if it on an evn number point, it moves on point. If the bug begins on point 1, what point will it be on after 2007 jumps?
It starts one 1.
Notice how it moves.

1 (initial) --> 4 (1st) --> 3 (2nd) --> 1 (3rd)

And from here and one it will repeat in this cycle.

Thus,

4 (4th) --> 3 (5th) --> 1 (6th)
4 (7th) --> 3 (8th) --> 1 (9th)
4 (10th) --> 3 (11th) --> 1 (12th)
.......
4 (2005th) --> 3(2006th) --> 1(2007th)