2022 MMATHS Individual Round Problems/Problem 3
Problem
Luke and Carissa are finding the sum of the first 
positive integers by adding them one at a time. Luke forgets to add one number and gets an answer of 
. Carissa adds a number twice by mistake and gets an answer of 
. What is the sum of the number that Luke forgot and the number that Carissa added twice?
Solution 1
The sum of the first positive integers is 
. This means that Luke forgot to add 
and Carissa added the number 
twice. Therefore, the sum of the number that Luke forgot and the number Carissa added twice is 
.
~Arcticturn
