5

Part of 2011 May Olympiad

Problems(2)

tiling a nxn board with 6-tiles May Olympiad (Olimpiada de Mayo) 2011 L1 P5

Source:

Determine for which natural numbers

n

it is possible to completely cover a board of

n \times n

1 \times 1

squares, with pieces like the one in the figure, without gaps or overlays and without leaving the board. Each of the pieces covers exactly six boxes.
Note: Parts can be rotated. https://cdn.artofproblemsolving.com/attachments/c/2/d87d234b7f9799da873bebec845c721e4567f9.png

combinatoricsTilingtiles

14-digit numbers, divisible by 18 May Olympiad (Olimpiada de Mayo) 2011 L1 P5

Source:

We consider all

14

-digit positive integers, divisible by

18

, whose digits are exclusively

1

2

, but there are no consecutive digits

2

. How many of these numbers are there?

number theoryDigitsdivisible