Math and Logic Puzzles: Redux

[tris]

the dead man had a problem with adding to 100%

[tris]

Spoiler: alternatively

any number ending in 5 is an odd multiple of 5 and can be expressed as 5n where n is an odd integer. cubed, this becomes 125n³. as the product of odd numbers, this is also odd.

[tris]

i know this one hehe

[tris]

Spoiler:

assign a schedule of mathematicians, so they each get a day in each period of 100 days. if the mathematician enters the room on their day, they turn the light on. and the next one turns it off.

eventually

someone will have been after every other mathematician on their day. its going to take fucking forever tho

[tris]

probably much more efficient ways of doing that

[tris]

hehe

[tris]

Spoiler: easy variant

one person turns on the light every time they enter a dark room. everyone else turns off the light if it's on two times and then leaves it alone. once the one who turns on has seen the light go off 199 times, they know everyone has been in the room.