chapter 2 problem

[cj964]

Can anyone please advise how to solve this problem in chapter 2(addition and substraction)? The answer is page 33.


The pages of a book are numbered 1 through n. When the page numbers of the book were added, one of the page was mistakenly added twice, resulting in the incorrect sum of 1986. What was the number of the page that was added twice? (1986 AIME #6).

Thanks!

[yongcheng3315]

Can anyone please advise how to solve this problem in chapter 2(addition and substraction)? The answer is page 33.


The pages of a book are numbered 1 through n. When the page numbers of the book were added, one of the page was mistakenly added twice, resulting in the incorrect sum of 1986. What was the number of the page that was added twice? (1986 AIME #6).

Thanks!

Le x be the page number added twice.

we are given that 1 + 2 + 3 + …+ n + x = 1986

We know that 1 + 2 + 3 + …+ n  = N <= 1986 and we get that  62 (by trial and error) and it works.

So n = 62 and N = 1953.

1986 - 1953 = 33 which is the answer.

(Twenty more problem solving skills book page 210 having two solutions for this problem).