2024 AMC 10A Problem 20
Let be a subset of such that the following two conditions hold:
• If and are distinct elements of , then .
• If and are distinct odd elements of , then .
What is the maximum possible number of elements in ?
• If and are distinct elements of , then .
• If and are distinct odd elements of , then .
What is the maximum possible number of elements in ?
The numbers satisfy the conditions of the problem.
You should repeat the pattern from Hint 1.
We should prove that .
Prove that from to , you can select at most numbers.
To prove Hint 7, note that from each group of 3 consecutive elements, we can select at most one number.
If we select numbers from to using Hint 8, we must select , and similarly, we must select .
Then, by using the conditions of the problem:
Since we want to select elements, we must select two elements from
which is impossible.
Then, by using the conditions of the problem:
Since we want to select elements, we must select two elements from
which is impossible.
We can select at most two elements from .
(C) 608