MathDB

5

Part of 2008 May Olympiad

Problems(2)

3 pieces of 4 squares each for 7x7 board

Source: XIV May Olympiad (Olimpiada de Mayo) 2008 L2 P5

9/19/2022
Matthias covered a 7×77 \times 7 square board, divided into 1×11 \times 1 squares, with pieces of the following three types without gaps or overlaps, and without going off the board. https://cdn.artofproblemsolving.com/attachments/9/9/8a2e63f723cbdf188f22344054f364f1924d47.gif Each type 11 piece covers exactly 33 squares and each type 22 or type 33 piece covers exactly 44 squares. Determine the number of pieces of type 11 that Matías could have used. (Pieces can be rotated and flipped.)
combinatorics
25 coins on 16x16 board

Source: XIV May Olympiad (Olimpiada de Mayo) 2008 L1 P5

9/22/2022
On a 16x1616 x 16 board, 2525 coins are placed, as in the figure. It is allowed to select 88 rows and 88 columns and remove from the board all the coins that are in those 1616 lines. Determine if it is possible to remove all coins from the board. https://cdn.artofproblemsolving.com/attachments/1/5/e2c7379a6f47e2e8b8c9b989b85b96454a38e1.gif If the answer is yes, indicate the 88 rows and 88 columns selected, and if no, explain why.
combinatorics