Difference between revisions of "2006 UNCO Math Contest II Problems/Problem 2"
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==Solution== | ==Solution== | ||
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+ | We start by expanding <math>(a + 1)(b + 1)(c + 1)</math>, and in doing so we obtain <math>abc + ab + ac + a + bc + b + c + 1</math>. We then subtract <math>abc</math> from <math>abc + ab + ac + a + bc + b + c + 1</math>, to get <math>ab + ac + a + bc + b + c + 1</math>. We finally subtract <math>1</math> from this value, as the problem asks for how many integers are strictly in between, and we get our answer of <math>\boxed{ab + ac + bc + a + b + c}</math> as desired. | ||
==See Also== | ==See Also== |
Latest revision as of 20:02, 3 February 2017
Problem
If and are positive integers, how many integers are strictly between the product and ? For example, there are 35 integers strictly between and
Solution
We start by expanding , and in doing so we obtain . We then subtract from , to get . We finally subtract from this value, as the problem asks for how many integers are strictly in between, and we get our answer of as desired.
See Also
2006 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |