Difference between revisions of "2017 UNCO Math Contest II Problems/Problem 7"
(Created page with "== Problem == == Solution == == See also == {{UNCO Math Contest box|year=2017|n=II|num-b=6|num-a=8}} Category:Intermediate Number Theory Problems") |
(→Problem) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | A box of 48 balls contains balls numbered 1, 2, 3, . . ., 12 in each of four different colors. | ||
| + | Without ever looking at any of the balls, you choose balls at random from the box and put | ||
| + | them in a bag. | ||
| + | (a) If you must be sure that when you finish, the bag contains at least one set of five balls | ||
| + | whose numbers are consecutive, then what is the smallest number of balls you can put in the | ||
| + | bag? (For example, a set of balls, in any combination of colors, with numbers 3, 4, 5, 6, and 7 | ||
| + | is a set of five whose numbers are consecutive.) | ||
| + | (b) If instead you must be sure that the bag contains at least one set of five balls all in the same | ||
| + | color and with consecutive numbers, then what is the smallest number of balls you can put in | ||
| + | the bag? Remember to justify answers for maximum credit. | ||
== Solution == | == Solution == | ||
Revision as of 00:16, 20 May 2017
Problem
A box of 48 balls contains balls numbered 1, 2, 3, . . ., 12 in each of four different colors. Without ever looking at any of the balls, you choose balls at random from the box and put them in a bag. (a) If you must be sure that when you finish, the bag contains at least one set of five balls whose numbers are consecutive, then what is the smallest number of balls you can put in the bag? (For example, a set of balls, in any combination of colors, with numbers 3, 4, 5, 6, and 7 is a set of five whose numbers are consecutive.) (b) If instead you must be sure that the bag contains at least one set of five balls all in the same color and with consecutive numbers, then what is the smallest number of balls you can put in the bag? Remember to justify answers for maximum credit.
Solution
See also
| 2017 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
