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Algebra Level 3

Find the number of ordered pairs of integers ( a , b ) (a, b) that satisfy the inequality 1 < a < b + 2 < 10. 1 < a < b+2 < 10.


The answer is 28.

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Rohit Udaiwal by Rohit Udaiwal , 20, India

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1 solution

Rohit Udaiwal
Jan 1, 2016

b b can be anywhere from 1 to 7. As b b increases by 1, the number of values for a a also increases by 1. Thus, our answer is 1 + 2 + … + 7 = 28 1+2+\ldots+7=\boxed{28} .

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