2020 CIME I Problems
2020 CIME I (Answer Key) | AoPS Contest Collections | ||
Instructions
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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
.