Brain Teaser help

[uforgot]

I have to make up a test for our conference math competition. Every year I choose the brain teaser category because I love them. I usually dig in books, and I have a few for this year, but I'd also like to hear your favorite ones. I include ones that make you groan such as:

How much dirt is in a hole 3ft by 4 ft by 2 ft deep?

Answer: none. There is no dirt in a hole

And complicated math ones,
Diophantus's youth lasted 1/6 of his life. He had his first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of diophantus's life. Diophantus died 4 years after the death of his son. How long did Diophantus live?

answer: 84 years.

Anyone have some favorites?

[OakLeaf]

Well, here's one someone just forwarded me... it's probably making the rounds of the Internets... There are other questions, but this is the only math-related one.

This must be done in your head only .
Do NOT use paper and pencil or a calculator. Try it.

Take 1000 and add 40 to it. Now add another 1000 . Now add 30 .
Add another 1000 . Now add 20 . Now add another 1000
Now add 10. What is the total?

(Highlight answer below)


Did you get 5000? The correct answer is actually 4100.

[uforgot]

HAHA! I did it and came up with 4100, but I can see where a lot of people would think 5000. It's like the 6 divided by 1/2 and most people would say three when it's actually 12. All I could find to highlight was 5000. Then I found the rest of them. How did you do the highlight thing?

[Over50Newbie]

Claudia,

If you look closely, you will see that the font is just a very light blue. Then when you highlight over it, it just turns a darker blue so that you can see it.

Oakleaf - that is a great question. I did it and got 5000, and I just did it again with my 22 year old daughter, and she also got 5000!

Here is my favorite math "brain teaser" that I do with my middle school students:

This one is also done in your head and it is meant to be read aloud.

You are driving a bus. It has 12 people on it. At the first stop, you drop off 3 people and pick up 5. At the next stop, 2 more people get on. At the next stop, you drop off 8 and don't pick up anyone. At the next stop, you pick up 10 and drop off none. At the next stop nobody gets off and nobody gets on. At the last stop, 12 people get off, but only 1 gets on.

Now, here are two questions for you to answer:

1. What is the name of the bus driver?
2. How many stops did the bus make?

Answers:
1. The person answering the question is the bus driver because the brain teaser starts with "You are driving a bus."
2. The bus makes 6 stops.

Some people get the first answer. Nobody ever gets the second answer - they are too busy counting the number of people getting on and off the bus. As soon as you ask the second question, all you usually hear is a bunch of moans from your audience, as they realize they have been tricked.

Enjoy!

Lynette

[tantrumbean]

I like this one:

A posh restaurant's customer waited 40 minutes for the waiter to take her order. Finally she got up and left. The Head waiter asked her if she had paid her bill. She said no, and offered to write the Manager an explanation. She wrote

10004180204

[tantrumbean]

I like this one:

A posh restaurant's customer waited 40 minutes for the waiter to take her order. Finally she got up and left. The head waiter asked her if she had paid her bill. She said no, and offered to write the manager an explanation. She wrote

10004180204

[Over50Newbie]

Tantrumbean - I'm feeling pretty stupid, but...

I don't get it!

Lynette

[uforgot]

Tantrumbean - I'm feeling pretty stupid, but...

I don't get it!

Lynette

It's pretty cryptic:

One owes nothing for one ate nothing to owe for
1 00 0 4 1 8 0 2 0 4

Okay, I tried to line up the words and numbers but my post wont let me. one -1 owes -00 nothing -0 for -4 and so on.

[tantrumbean]

Ooops sorry, I was going to put the answer on, but was playing with the pale yellow fonts and messed it up... Heyho, uforgot provided it anyway! (And I didn't read the bit about them having to be math related either)

[alpinerabbit]

This is a lateral thinking teaser:


Caesar lies dead on the floor. Cleopatra jumped out of the window.
On the floor, there is broken glass and a puddle of water.


What happened?

[uforgot]

Ooops sorry, I was going to put the answer on, but was playing with the pale yellow fonts and messed it up... Heyho, uforgot provided it anyway! (And I didn't read the bit about them having to be math related either)

Oh, it's okay if it isn't math related. I like them all. I'll use the math ones on my test and enjoy the others! Sorry I couldn't resist answering and hey, I waited almost a day! The Caesar/Cleopatra is going on my board today.

Here is a favorite of mine. An oldie classic:

As I was going to St. Ives,
I met a man with seven wives,
Seven wives had seven sacks,
Seven sacks had seven cats,
Seven cats had seven kits,
Kits, Cats, Sacks, Wives,
How many were going to St. Ives?

[Over50Newbie]

Aaahh, now I see...

Thanks, uforgot!

Okay, here's one more. This one is much more math related:

Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent 9 years as an old man, then how many years did he spend as an active man?

Highlight to find answer.

Answer
36

Solution:

Fraction of life as a boy = 1/4
Fraction of life as a youth = 1/8
Fraction of life as an active man = 1/2
Fraction of life as boy, youth and active man = 1/4 + 1/8 + 1/2 = (2 + 1 + 4)/8 = 7/8
Fraction of life as an old man = 1 − 7/8 = 1/8
Thus, one-eighth of Man Wrinkle's life (as an old man) is 9 years.
So, Man Wrinkle's Age = 72 years.

[tantrumbean]

This is a lateral thinking teaser:


Caesar lies dead on the floor. Cleopatra jumped out of the window.
On the floor, there is broken glass and a puddle of water.


What happened?

Caesar is the goldfish, Cleopatra the cat!