A U2 Concert

U2 has a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them.

The flashlight must be walked back and forth. It cannot be thrown and other tricks like that are not needed to solve the problem. The solution is simply a matter of allocating resources in a certain order. Each band member walks at a different speed. A pair must walk together at the rate of the slower man’s pace:

Bono: 1 minute to cross
Edge: 2 minutes to cross
Adam: 5 minutes to cross
Larry: 10 minutes to cross

For example: if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission.

This is one of my favorite brain teasers and I want to give you the satisfaction of figuring it out on your own. If you’re having a hard time, here’s a hint: There is a valid answer that doesn’t require tricks like throwing the flashlight or shining it backwards or having some other means of moving the flashlight.

There’s an assumption people often make that keeps them from solving this. Two members cross the bridge each time, but neither one of the two who crossed necessarily need to return. Think about how that would be possible. If you’re still stuck, use objects to simulate their movements. Use whatever you have laying around – pens, paper, erasers – and move them back and forth. Good luck!

Posted in Brain Teasers

Ethan’s Grand Night Out

Ethan was going for a night out but his key fob battery had died and the button wouldn’t unlock his car door. How was he able to get in?

He used the key embedded in the key fob.

Posted in Brain Teasers

Eyes That Don’t See

Most of you have two eyes. I only have one.
Most of you have eyeballs. I do not.
Your eyes aren’t dangerous, neither are mine.
But all together, I am extremely dangerous.
You can see things with your eyes.
I can’t see anything, even though the air is clear where my eye is.

What am I?

The eye of a tornado or hurricane. Could also be the eye of a needle.

Posted in Riddles
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The Ages of a Prince and Princess

A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess’s age was half the sum of their present ages.

What are their ages?

This one took a while to figure out and there are numerous valid ways of finding the answer.

Here is the solution I came up with

I created the following table from the riddle:

  Current Future Past
Princess x 2z (x+y)/2
Prince y x z

I then created three equations, since the difference in their age will always be the same.
d = the difference in ages
x – y = d
2z – x = d
x/2 + y/2 – z = d

I then created a matrix and solved it using row reduction.

x y z
1 -1 0 d
-1 0 2 d
.5 .5 -1 d

It reduced to:

x y z
1 0 0 4d
0 1 0 3d
0 0 1 5d/2

This means that you can pick any difference you want (an even one presumably because you want integer ages).
Princess age: 4d
Prince age: 3d

Ages that work

Princess Prince
4 3
8 6
16 12
24 18
32 24
40 30
48 36
56 42
64 48
72 54
80 60

To see other solutions check out the comments from when I posted this on my blog.

Posted in Brain Teasers

Probability That Both Children Are Girls

Walking down the street one day, I met a woman strolling with her daughter. “What a lovely child,” I remarked. “In fact, I have a younger child as well,” she replied.

What is the probability that both of her children are girls?

1/2 probability. This has been know to cause raging debates and is known as one of the variations of the Boy or Girl paradox. This variation is more straightforward because knowing the position of the child leaves only two possibilities – the other child is a boy or a girl, each of which have a 1/2 probability.

Another variation of this can be found here.

Posted in Brain Teasers

I Turn Around Once

I turn around once,
What is out will not get in.
I turn around again.
What is in will not get out.

What am I?

A key.

Posted in Riddles
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Three Pills From the Doctor

Your doctor gives you three pills and tells you to take one every half hour. How much time will have passed by the time you’ve taken all three pills?

One hour. You take the first pill, then wait a half hour and take the second pill, then at the hour mark you take the third and last pill.

Posted in Brain Teasers

What is HIJKLMNO?

HIJKLMNO

What 5-letter word does this represent?

Water. Or literally, H to O, which sounds the same as H2O.

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Pitching On The Merry-Go-Round

Everly and I were playing on the merry-go-round at the local park. It was very large and we stood on opposite sides. As we spun the merry-go-round counter-clockwise, I threw a ball to Everly. Did the ball go to Everly, to the right or left of them?

Since the merry-go-round had moved while the ball was traveling to Everly the ball went to the right of them.

Posted in Brain Teasers

What Boys Use, Girls Like and Parents Hate

Boys use it, girls like it, parents hate it. What is this 5-letter word?

The phone.

Posted in Riddles