MathDB

12

Part of 2014 ASDAN Math Tournament

Problems(2)

2014 General #12

Source:

7/5/2022
Consider a rectangular tiled room with dimensions m×nm\times n, where the tiles are 1×11\times1 in size. Compute all ordered pairs (m,n)(m,n) with m≤nm\leq n such that the number of tiles on the perimeter is equal to the number of tiles in the interior (i.e. not on the perimeter).
2014General Test
2014 Team #12

Source:

7/1/2022
Find the last two digits of (200100)\tbinom{200}{100}. Express the answer as an integer between 00 and 9999. (e.g. if the last two digits are 0505, just write 55.)
2014team test