We want to cover a table of size with dominoes of the following shape
(can also be reflected or rotated),
where the dominoes may overlap or extend over the edges of the table.
At least how many dominoes do we need?
, 2013
Solution
We need at least 5 dominoes. If it is possible to cover the table with four dominoes, then they cannot overlap and cannot extend over the edges of the table since four dominoes cover exactly 16 squares. In this case there are only two possible ways of covering the top left corner as shown in the figures. But in both cases the field marked with * cannot be covered.
It is easy to see that 5 dominoes suffice as demonstrated by the figure above.
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.