Jumping on the number line
Probability
Level
3
A Bug is sitting on the origin of the number line. Each step he jumps 3 units or 5 units to the right. There is a mine at all integer points that are neither divisible by 3 nor 5, and Bug wants to avoid all those points. His house is at 120. How many ways can he jump back to his home?
The answer is 256.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
L.C.M of 3 & 5 is 15. So bug has to cover 15 units(continuously) by taking one of the jumps i.e. either by jumps of 5 units or 3 units to avoid mines. Like it can cover 120 units at 8 stretches. Since in each stretch it has got 2 options to follow the required number of ways is 2^8 i.e. 256