perplexus.info :: Just Math : Number around a circle

Number around a circle (Posted on 2025-04-27)

100 numbers were written around a circle. The sum of the 100 numbers is equal to 100 and the sum of six consecutive numbers is always less than or equal to 6. The first number is 6. Find all the numbers.

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Possible solution

| Comment 1 of 2

If negative numbers are permitted then one solution (I suspect the only solution) is to alternate 6 and -4. That way every two numbers sum to 2, so the total sum of 100 numbers is 100. And every sum of 6 consecutive numbers is 6.

Not a formal proof that this is the only solution.

Posted by Larry on 2025-04-27 10:09:22

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info