Difference between revisions of "2022 MMATHS Individual Round Problems"
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==Problem 3== | ==Problem 3== | ||
Luke and Carissa are finding the sum of the first <math>20</math> positive integers by adding them one at a time. Luke forgets to add one number and gets an answer of <math>207</math>. Carissa adds a number twice by mistake and gets an answer of <math>225</math>. What is the sum of the number that Luke forgot and the number that Carissa added twice? | Luke and Carissa are finding the sum of the first <math>20</math> positive integers by adding them one at a time. Luke forgets to add one number and gets an answer of <math>207</math>. Carissa adds a number twice by mistake and gets an answer of <math>225</math>. What is the sum of the number that Luke forgot and the number that Carissa added twice? | ||
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| + | [[2022 MMATHS Individual Round Problems/Problem 3|Solution]] | ||
Revision as of 20:16, 18 December 2022
Problem 1
Suppose that 
and 
. Compute 
.
Problem 2
Triangle 
has 
and 
. Points 
and 
are the reflections of 
over 
, over , over 
, over , over , and over , respectively. Find the area of hexagon 
.
Problem 3
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?
