Question

on the table

Answer 1

Ten girls, numbered from 1 to 10, sit at a round table, in a random order. Each girl then
receives a new number, namely the sum of her own number and those of her two neighbours.
Prove that some girl receives a new number greater than 17.

Answer 2

@Jonask If let's say the students are sitting around the table in order. Then the number 3 girl is between 2 and 4 hence her new number would be 2 + 4 = 6. Does this mean that if I were to now find the new number of the girl number 2, I would be adding 1 + 6 instead of 1 + 3?

Answer 3

Or do you keep going with only the numbers that they previously had.

Answer 4

Btw, why are you doing problems from the harmony south african olympiad? lols..

@Jonask

Answer 5

lol i am from south africa and you??? and i like olympiad problems

Answer 6

Divide the nine girls with numbers 2 to 10 into three groups of
three: the three girls to the left of no 1, the three girls to the right of no 1, and the three girls opposite no 1. The total sum of their numbers is 54, so the sum of at least one group must be at least 18. Therefore the new number of the girl in the middle of that group is at least 18.

Answer 7

i think you need to consider 1+6