2020 CIME I Problems
| 2020 CIME I (Answer Key) | AoPS Contest Collections | ||
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Instructions
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to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.Problem 1
A knight begins on the point 
in the coordinate plane. From any point 
the knight moves to either 
or 
. Find the number of ways the knight can reach 
.
Problem 2
At the local Blast Store, there are sufficiently many items with a price of 
for each nonnegative integer 
. A sales tax of 
is applied on all items. If the total cost of a purchase, after tax, is an integer number of cents, find the minimum possible number of items in the purchase.
Problem 3
In a math competition, all teams must consist of between 
and 
members,
inclusive. Mr. Beluhov has 
students and he realizes that he cannot form
teams so that each of his students is on exactly one team. Find the sum of all
possible values of .
