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Monday, January 21, 2008

5 Point Star

Fill in the ten circles with numbers so that the sums of numbers along each of the five lines are the same value. The numbers do not need to be contiguous. What is the smallest sum you can make using whole numbers? Can you find a solution with sums less than 41?



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7 comments:

Erik said...

Here are some numbers to get you started:

         60

56   63  66   69

     59    51
         62

    72      77


These numbers sum to 254 on each line. I'm sure you can do better.

Anonymous said...

yes, mr genious.

Just take 50 off every number, then you've got 54 on every line.

that was damn easy.

Erik said...

Since that was so easy, take another look at the original question and see if you can find a solution where each sum is less than 41. Can you prove that this is the smallest sum possible using positive integers?

Anonymous said...

Just put the same number in every circle and the sum will always be the same! ;)

Anonymous said...

PUT '1' IN EACH CIRCLE, THAT WAY IT ALWAYS ADDS UP TO '4' ALONG EACH LINE.

WHAT DOES CONTIGUOUS MEAN????

Elliot said...

Hi I have a similar puzzle but the question is different, wondering if anyone can find the answer for me. The star is the same but the question is:
Place the numbers 1 to 10 along the sides of the star so that each side adds up to 22.
Thanks :D

Alex G said...

yep. I got 28 without repeated numbers.

14
12 1 4 11
3 2
5
10 8