Points on a circle

Question

36 points are marked, equally spaced, on the circumference of a circle. Some of the points are marked with crosses in such a way that the distances between every two consecutive crosses are all diffrent. What is the maximum number of crosses that can be made?

Ive tried individual cases but, i havnt been able to do much else. I tried finding a pattern with 1 point, 2 points, 3 points etc but couldnt find anything.

Answer 1

Hint:

• You want to put as many crosses as you can, so the distances has to be as small as possible.
• The smallest distance is $1$ (that is the length of one side of your 36-gram).
• When you have used distance $1$, the next smallest distance you can use is $2$ and then $3$ and so on...
• What can you say about the total sum of distances between crosses?

I hope this helps ;-)

Answer 2

The answer is 7.

Since we need to have as small distance as possible between succeeding points try incrementing each distance by one starting with 1.

X-1-X-2-X-3-X-4-X-5-X-6-X-8

1+2+3+4+5+6+8=29

29+7(x's)=36 points.

since 1+2+...+7+7(x's) is less than 36 (initial try) try adding one unit distance to the last distance making it 8.