Pigeonhole Principle

True or False: Given any 5 integers, there must be two whose difference is divisible by 4.

• True

• False

Tags

CCSS.6.NS.C.6A

How many people must be in a room to guarantee that 3 of them were born in the same month?

• 25

• 36

• 37

• 93

True or False: If 42 poker chips are distributed among 4 players, there must be some player that receives at least 12 chips.

• True

• False

Tags

CCSS.4.NBT.B.6

By the pigeonhole principle, if 40 coins are distributed among 7 boxes, then there must be some box with at least ___ coins.

• 6
• 5
• 7
• 8

In a dark room there are 12 red and 12 blue socks in a drawer.

At least how many socks do you need to take out of the drawer so that there would be at least two socks of the same color for sure?

• 3

• 13

• 25

At least how many whole numbers should be written down so that there would be two among them for sure the difference of which is divisible by 8?

• 8

• 9

• 2