Question 10
The integers $2003$ from $1$ to $2003$ are written on the board. Lucas must delete $90$ numbers. Next, Mauro must choose $37$ from the numbers that remain written. If the $37$ numbers Mauro chooses form an arithmetic progression, Mauro wins. If not, Lucas wins.
Decide if Lucas can choose the $90$ numbers to clear so that victory is assured.
Decide if Lucas can choose the $90$ numbers to clear so that victory is assured.