3

Part of 2020 May Olympiad

Problems(2)

There is a box with 2020 stones

Source: May Olimpiad 2020 L2 P3

There is a box with 2020 stones. Ana and Beto alternately play removing stones from the box and starting with Ana. Each player in turn must remove a positive number of stones that is capicua. Whoever leaves the box empty wins. Determine which of the two has a strategy winner and explain what that strategy is.

Note:

A positive integer is capicua if it can be read equally from right to right. left and left to right. For example, 3, 22, 484 and 2002 are capicuas.

ant moving 1N, 2E, 3S, 3W, 5N, 6E, ...,41N (2020 May Olympiad L1 P3)

Source:

A clueless ant makes the following route: starting at point

A

1

2

3

4

cm west, immediately

5

cm north, continues

6

cm east, and so on, finally

41

cm north and ends in point

B

. Calculate the distance between

A

B

(in a straight line).

geometrydistance