Challenging 6'th grade question for math enthusiasts!

Taken from "Russian math olympiads in Moscow 1993-2002" by N.Aghanov and O.Podlipsky.

Given at the regional stage of 1994.

The pages of a book are numbered from the first to the very last. The hooligan Vasia ripped 25 pages of the said book and added the numbers on these pages. He got 1994. When Kolia found out about this, he instantly knew that Vaisa had added the numbers wrong. Explain why Kolia is right.

Question

Challenging 6'th grade question for math enthusiasts!

Taken from "Russian math olympiads in Moscow 1993-2002" by N.Aghanov and O.Podlipsky.

Given at the regional stage of 1994. 

The pages of a book are numbered from the first to the very last. The hooligan Vasia ripped 25 pages of the said book and added the numbers on these pages. He got 1994. When Kolia found out about this, he instantly knew that Vaisa had added the numbers wrong. Explain why Kolia is right.

rational · Answer

the sum better be odd

anonymous · Answer

^_^

anonymous · Answer

No matter what pages you rip out off a book, the numbers on those pages will always be consecutive. An odd and an even page added together = and odd number. Since there are 25 pages we have 25 odd numbers - which added together result in an odd number. Which means it can't be 1994.

anonymous · Answer

I'm going for another one. This one requires a bit of physics explanation but I'll try to leave the physics aside.