Question

a beetle sets out on a journey. on the first day it crawls 1m in a straight line. on the second day it makes a right-angled turn (in either direction) and crawls 2m in a straight line. on the third day it makes a right-angled turn (in either direction) and crawls 3m in a straight line. this continues each day with the beetle making a right-angled turn ( in either direction and crawling 1m further than it did the day before. what is the least number of days before the beetle could find itself stopped at its starting point?

Answer 1

7

Explanation:

The signed sum of sequential odd numbers must be zero, as must the signed sum of sequential even numbers.

The minimum number of sequential even numbers that have a sum of 0 is 3: 2+4-6 = 0.

The minimum number of sequential odd numbers with a sum of zero is 4: 1-3-5+7=0.

Since we start with an odd number, we can get these sets of numbers in 7 days. The attached diagram shows one possible route.