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 |