Easier Alternatives to Tedious Tasks

[Ilikebugs]

View attachment 6362 This seems really tedious, is there a better way than powering through/?

 

[HallsofIvy]

Since the cards all started with the red side up, that would be the cards that are turned over an even number of time- 0, 2, or 4. Since we turn over every card that is a multiple of 2, then 3, then 4, then 5, the cards that are never turned over are those that are that are not multiples of any of those- 7, 11, 13, 17, 19, etc. That include all prime numbers larger than 5 but also those that are multiples of 7, 11, etc. I will let you work out how many there are.

The cards that are turned over exactly twice are those that are even and a multiple of 3 but not 4 or 5- 6, 18, etc. Of course any multiple of 4, other than those that are also multiples of 3 and/or 5. Also those that are multiples of 2 and 5 but not 3 and 4, as well as those that are multiples of 3 and 5 but not 2.

 

[Ilikebugs]

is the answer 52?