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

Only Found In The Past

You will only ever find me in the past. I am created in the present but the future can never taint me. What am I?

History

Posted in Riddles
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Losing Ten Minutes An Hour

A clock loses exactly ten minutes every hour. If the clock is set correctly at noon, what is the correct time when the clock reads 3:00pm?

3:36pm. For every 60 minutes of real time, the clock moves 50 minutes. Put another way, 60/50 = 1.2 real minutes per slow-clock minute.

In order for the clock to show 3:00pm, 180 of its slow minutes have to pass. 1.2 * 180 clock minutes = 216 real minutes or 3 hours and 36 minutes.

Posted in Brain Teasers

Messy Math

What is the answer to this problem?

48 / 2(9 + 3) = ?

It depends. Usually, math has one right answer, but in this case, the order of operations can get a little quirky.

There are two ways to solve this. First, like so:
48 / 2 × (9 + 3) = ?
48 / 2 × (12) = ?
24 × 12 = 288

But another, arguably valid way is:
48 / 2 × (9 + 3) = ?
48 / 2 × (12) = ?
48 / 24 = 2

Thanks to KnowYourMeme for providing a great overview on this one. Math StackExchange has more discussion.

Posted in Brain Teasers

Colored Houses

A red-house is made of red bricks, has a red wooden door and a red roof. A yellow-house is made of yellow bricks, has a yellow wooden door and a yellow roof. What is a green-house made of?

Glass.

Posted in Brain Teasers

Doesn’t Fly Even With Wings

I have four wings but cannot fly,
I’ve never laughed nor will ever cry,
As much as I’d love to leave the ground,
I toil away with nary a sound.

What am I?

A few windmills

A windmill. The typical windmill, like the ones Don Quixote chased, have four vanes or sails. You might even say they look like wings. Windmills don’t have emotions, so they can’t laugh or cry. And since they don’t have actual wings, windmills don’t get off the ground. A well-oiled little bugger won’t make a peep.

Posted in Riddles
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None There’ll Be

There is a word of letters three,
Add one letter to it and none there’ll be.

What is the word?

One. Add an ‘n’ to get none.

Posted in Riddles

What Can Be Swallowed

What can be swallowed, But can also swallow you?

Pride.

Posted in Riddles

Eight Eleven Five Sequence

Which two numbers are missing and where do they go in the sequence?

8, 11, 5, 14, 1, 7, 6, 10, 13, 3, 12, 2

The missing numbers are 4 and 9. The list is sorted alphabetically by the English spelling of the numbers, so four belongs after five and nine comes after fourteen.

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A Bridge to Switzerland

During WWII, there was a bridge connecting Germany and Switzerland, and on the German side, there was a sentry tower with a guard in it. He would come out every three minutes to check on the bridge, and he had orders to turn back anyone who tried to get into Germany, and shoot anyone trying to escape without a pass. There was a woman who desperately needed to get into Switzerland, and she knew she didn’t have time to get a pass. It would take her at least six minutes to cross the bridge, but she managed to do it. How?

She walked on the bridge towards Switzerland for 3 minutes and just as the guard was about to come out, she turned around walking back to Germany. The guard saw her and asked for her pass but she didn’t have one and was sent back (or what the guard thought was back) to Switzerland. In her case it was the very country she wanted to go to.

Posted in Brain Teasers