1999 numbers are placed along the circumference of a circle. When any four successive numbers are added, the total is always 28. What are these 1999 numbers? Find all possible solutions.
* ADDITIONAL NOTE: I have a feeling that they are all 7... but I can't prove it... if you could, that would be a great help.
Thanks heaps guys... :)
2007-07-16 03:01:31 · 1 answers · asked by helpme.com 1 in Science & Mathematics ➔ Mathematics
Pick any 4 numbers in a row. If we shift it by 1, in order for it to also sum to 28, the number added to the set has to be the same as the one dropped from it. Hence the 1999 numbers has to be a repeating sequence of 4 numbers. But 4 doesn't divide into 1999, so they have to be all 7.
The problem is more complicated if we allow negative integers, but the modulo still has to repeat in sets of 4.
2007-07-16 03:49:51 · answer #1 · answered by Scythian1950 7 · 1⤊ 0⤋