Difference between revisions of "2022 AIME II Problems/Problem 14"
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==Solution 1== | ==Solution 1== | ||
| − | Notice that <math>a</math> must equal to <math>1</math>, or else the value <math>1</math> cent isn't able to be represented. At least <math>b-1</math> | + | Notice that <math>a</math> must equal to <math>1</math>, or else the value <math>1</math> cent isn't able to be represented. At least <math>b-1</math> numbers of <math>1</math> cent stamps will be needed. Using at most <math>c-1</math> stamps of value <math>1</math> and <math>b</math>, it is able to have all the values from <math>1</math> to <math>c-1</math> cents. |
| − | To be continued | + | To be continued...... |
~[https://artofproblemsolving.com/wiki/index.php/User:Isabelchen isabelchen] | ~[https://artofproblemsolving.com/wiki/index.php/User:Isabelchen isabelchen] | ||
Revision as of 12:03, 19 February 2022
Problem
For positive integers 
, 
, and 
with 
, consider collections of postage stamps in denominations , , and cents that contain at least one stamp of each denomination. If there exists such a collection that contains sub-collections worth every whole number of cents up to 
cents, let 
be the minimum number of stamps in such a collection. Find the sum of the three least values of such that 
for some choice of and .
Solution 1
Notice that must equal to 
, or else the value cent isn't able to be represented. At least 
numbers of cent stamps will be needed. Using at most 
stamps of value and , it is able to have all the values from to cents.
To be continued......
See Also
| 2022 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
