Novels are not just for reading!
Number Theory
Level
2
There is a paperback novel. When we tear a page from the novel, the sum of the remaining page no.'s equals 15,000. What must be the smallest of the two page no.'s on the torn page?
The answer is 25.
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If the book has n pages, the sum of the pages is n(n+1)/2 Therefore, if you take page a and a+1, we get: n(n+1)/2 -a-(a+1)=15000
Rewrite as: 4a = n(n+1)-30002 > 0
That means n>=173
For n = 173 the expression yields: 4a = 100 a=25