2006 UNCO Math Contest II Problems/Problem 2: Difference between revisions
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==Solution== | ==Solution== | ||
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 19:02, 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 | ||
