Question 169
Five children sit around a circular table. Each child chooses a positive integer and tells it to the others. Then each child does the following computation: they add the numbers of the two children on their left, subtract the sum of the numbers of the other two children on their right, and multiply this difference by their own number, thus obtaining their final result.
Prove that the sum of the final results of all the children is a fixed value that does not depend on the numbers the children initially chose, and then determine this value.
Prove that the sum of the final results of all the children is a fixed value that does not depend on the numbers the children initially chose, and then determine this value.