Difference between revisions of "2024 AMC 10B Problems/Problem 16"
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Revision as of 09:40, 14 November 2024
Contents
Problem
Jerry likes to play with numbers. One day, he wrote all the integers from 
to 
on the whiteboard. Then he repeatedly chose four numbers on the whiteboard, erased them, and replaced them by either their sum or their product. (For example, Jerry's first step might have been to erase , 
, 
, and 
, and then write either 
, their sum, or 
, their product, on the whiteboard.) After repeatedly performing this operation, Jerry noticed that all the remaining numbers on the whiteboard were odd. What is the maximum possible number of integers on the whiteboard at that time?
Solution 1
Consider the numbers as 
. Note that the number of odd integers is monotonously decreasing.
We need to get rid of 
's, so we either add or multiply the s together to get 
To get rid of the final , we need to consume three other 's to result in one . Thus the answer is 
,
~Mintylemon66
Solution 2
See also
| 2024 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
