2025 AMC 10A Problems/Problem 21

A set of numbers is called - if whenever and are (not necessarily distinct) elements of the set, is not an element of the set. For example, and the empty set are sum-free, but is not. What is the greatest possible number of elements in a sum-free subset of ?

Solution 1

Let our subset be If we add any one element from the set we will have to remove at least one element from our current subset. Hence, the size of our set cannot exceed

~Tacos_are_yummy_1

Solution 2

Let our subset be Since odd numbers + odd numbers will always sum to an even number, this subset holds true. Leo, the addition of any even number will result in a violation of the rule, so the maximum number of elements is

~KMS888

Solution 3 (???)

I'm kinda surprised that this question is just the copy-and-paste version of 2022 10B Problem 14. This problem is easier yet it's at problem 21. Nice problem quality you got there, huh, just adding a fancy definition, and yay, you got a brand new problem!

https://artofproblemsolving.com/wiki/index.php?title=2022_AMC_10B_Problems/Problem_14

~metrixgo

It’s just the number of elements if you only put the odd numbers in like what this should’ve been problem 10 not that semicircle problem

See also

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