Difference between revisions of "2016 UNCO Math Contest II Problems/Problem 4"
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== Problem == | == Problem == | ||
| + | Number Sieve | ||
| + | How many positive integers less than 100 are divisible by exactly two of the | ||
| + | numbers 2, 3, 4, 5, 6, 7, 8, 9? For example, 75 is such a number: it is divisible by 3 and by 5, but | ||
| + | is not divisible by any of the others on the list. (If you show the integers you find, then you | ||
| + | may be assigned partial credit if you have accurately found most of them, even if you do not | ||
| + | find all of them.) | ||
== Solution == | == Solution == | ||
| + | There are eighteen such numbers: <math>4, 9, 10, 14, 15, 21, 27, 35, 44, 50, 52, 68, 75, 76, 81, 92, 98, 99</math> | ||
== See also == | == See also == | ||
{{UNCO Math Contest box|year=2016|n=II|num-b=3|num-a=5}} | {{UNCO Math Contest box|year=2016|n=II|num-b=3|num-a=5}} | ||
| − | [[Category:]] | + | [[Category: Intermediate Number Theory Problems]] |
Latest revision as of 03:02, 13 January 2019
Problem
Number Sieve
How many positive integers less than 100 are divisible by exactly two of the numbers 2, 3, 4, 5, 6, 7, 8, 9? For example, 75 is such a number: it is divisible by 3 and by 5, but is not divisible by any of the others on the list. (If you show the integers you find, then you may be assigned partial credit if you have accurately found most of them, even if you do not find all of them.)
Solution
There are eighteen such numbers: 
See also
| 2016 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
