Hats and Wizards
Venn Diagram
Egyptian Multiplication
Binary Numbers
Bonus: Exponents
100
There are three hats in a closet: one green, two yellow. Without looking, Alice, Bob and Carl each put one hat on their own head. If Alice looks at Bob and sees that he is wearing a green hat, does Alice know what color her own hat is?
Yes!
100
At the dog pound there are 40 dogs. If 22 dogs have spots and 30 dogs have short hair, what is the fewest number of dogs that can have both short hair and spots?
12
100
Use Egyptian multiplication to multiply 42 times 12. Show your work.
504
100
Write 12 and 42 in binary.
11002 and 1010102
100
(410)3 = 4?
(410)3 = 430
100
Again, there are three hats. Again, without looking, Alice, Bob and Carl each put one hat on their own head. I tell them: "Raise your hand if you do not know the color of your own hat." How many kids raise their hands?
None!
100
Ten friends go out for ice cream. 7 put chocolate sauce on top. 5 put marshmallows on top. 4 put nuts on top. If everyone put at least 1 item on top, but no one put exactly 2 items on top, how many people piled three things on top of their ice cream?
3
100
Use Egyptian multiplication to multiply 69 times 11. Show your work.
759
100
Write 11 and 69 in binary.
10112 and 10001012
100
Which is bigger?
164 85
164
100
Now there are five hats in the closet: three yellow, two green. Without looking, Alice, Bob and Carl each put one hat on their own head. If Alice knows her color, what color must Bob be wearing on his head?
Green!
100
150 people at a concert were asked if they knew how to play piano, drums or guitar. Draw a Venn Diagram, filling in every detail.
18 people could play none of these instruments.
10 people could play all three of these instruments.
77 people could play drums or guitar but could not play piano.
73 people could play guitar.
49 people could play at least two of these instruments.
13 people could play piano and guitar but could not play drums.
21 people could play piano and drums.
100
Use Egyptian Multiplication to multiply 55 times 18. Show your work.
990
100
Write 18 and 55 in binary.
100102 and 1101112
100
Which is bigger?
156・86 126・66
156・86
100
Again, five hats. Again, three yellow, two green. I ask Alice if she knows her color and she says "no". I now ask Bob if he knows his color. Does he?
It depends!
100
D is A’s grandfather
100
How many 1x1 square shapes can be used to make a 2x2 square?
4
100
I have good news. On Monday, I told 2 friends. On Tuesday, they each told 2 friends. On Wednesday, those new friends each told 2 friends. If this pattern continues, how many people will have heard my news in total by Friday?
63
100
4999+ 4999+4999+ 4999 = 4?
4999+ 4999+4999+ 4999 = 41000
100
Carl has been listening. He heard Alice say that she does not know her color. He heard Bob say that he does not know his color. I now ask Carl if he knows his own color. He says yes. What color hat is he wearing?
Yellow!
100
Oops! There's nothing here!
:)
100
How many 1x1 square shapes can be used to make a 3x3 square?
9
100
What is 10010 in Base 2? BONUS: What about Base 3?
11001002 and BONUS: 102013
100
36・47・94 = ?14*__
36・47・94 = 614*__