Answer to Question #332750 in Trigonometry for Shang

Question

The mayflower is the Massachusetts State flower and Nova Scotia's provincial flower. It has five petals. Imagine that the petals are numbered 1, 2, 3, 4 and 5 in a clockwise order. A ladybug has landed on petal number 1. She begins to jump in a counterclockwise direction from one petal to another, around the flower. When she jumps from an odd-numbered petal, she skips a petal. When she jumps from an even-numbered petal, she jumps to the next petal. Since it is the year 2018, she has decided to make 2018 jumps. What number petal will she be when she stops jumping?

Answer 1

If the ladybug starts from petal #1 and jumps as shown in the picture, then her petal numbers will be 1,4,3,1,4,3,1,......etc.

That is, after every 3 jumps, the ladybug will return to its original position. That is, it will be on petal No. 1 after 3 jumps, after 6, 9, 12, 15, ...... 2013, 2016 (since 2016 is completely divided by 3).

So we have this ratio:

2016--1

2017--4

2018--3

Answer: 3 petal