1980 Canadian MO Problems

Problem 1

If is the decimal expansion of a number in base , such that it is divisible by , determine .

Solution

Problem 2

The numbers from to are printed on cards. The cards are shuffled and then laid out face up in rows of cards each. The cards in each row are rearranged to make them increase from left to right. The cards in each column are then rearranged to make them increase from top to bottom. In the final arrrangement, do the cards in the rows still increase from left to right?

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Resources

1980 Canadian MO