Question

Counting on Ninja Turtles

Joanne sets up her teenage Mutant Ninja Turtles in a big circle, spacing each turtle at an
equal distance from its neighbors. She then begins counting them in order around the circle,
but she loses track of where she started before she finishes counting. Then she notices
that the sixth turtle is directly opposite the seventeenth turtle, and she realizes that she can
still figure out how many turtles are in the circle. How many turtles are in the circle?

Answer 1

there are 22 turtles in the circle

Step-by-step explanation:

We are told all the turtles are evenly spaced and that 6th turtle is opposite the 17th one.

Now, if we count 6, 7, 8, up to 17, we'll get 12 turtles.

Now, since 6th and 17th are opposite to each other, then 10 turtles are between them. so the same number of turtles should stand in other side too. Thus, there are 10 turtles, evenly spaced, on either side of 6 and 17, which

are at opposite ends of a diameter.

Of the 10 turtles on the other side, we know there is 1,2,3,4,5.

That leaves 5 more and they are greater than 17, starting

with 18, we go 18,19,20,21,22

Thus, there are 22 turtles in the circle