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

Add An A But Sounds The Same

What word starts with the letter “I”, becomes another word by adding the letter “A” yet has the same pronunciation?

Isle, Aisle

Posted in Brain Teasers

What is the Chance That You’ll Be Correct?

If you choose an answer to this question at random, what is the chance that you will be correct?

a) 25%
b) 50%
c) 60%
d) 25%

This is becomes a self-referential paradox. Both A and D would be correct if there were four unique answers, but since A and D are the same answer, the chance that you would choose a correct answer is 50%, which makes B correct. But if there’s only one correct answer, the odds of choosing the correct one at random goes back to 25%. And around and round you go.

There’s a lot of discussion at Richard Wiseman’s blog and more at Lifehacker, where I first saw this.

Posted in Brain Teasers

Ten White Man On A Dirt Road

Ten white men standing on a dirt road.
Killed by three eyes as black as night.

What happened?

Someone bowled a strike. The ten white men are the pins, the dirt road is the bowling alley (it’s not dirt, but it’s the color of dirt, and if it said a smooth wooden alley it wouldn’t be much of a riddle). Three eyes as black as night are the finger holes in the bowling ball.

Posted in Riddles

What Letter Comes Next?

The letters in this series are ones that don’t begin something. Figure out what that something is, and what letter comes next.

B E J ?

Q. The thing they don’t begin is states in the United States of America. The final three letters in the series are X, Y and Z.

Posted in Brain Teasers

More Than a Few

Nothing specific,
but more than a few.
This many clustered
together will do.

Bunch. It’s a vague term that means more than a few. And clustered items like bananas, grapes or celery come in bunches.

By Sef Daystrom

Posted in Riddles

Same Three Digits with Sum of 800

When Florence and Willie finished playing darts, they proudly announced that their 3-digit scores added up to exactly 800 points. Furthermore, each of their scores shared the same 3 digits, without any repeating digits.

What were their two scores?

364 and 436.

You could figure this out mathematically, but instead, I plugged in digits that added up to 10 for the first column, 9 for the second column (since you carry the 1) and 7 for the third column (again, because you’re carrying the 1).

Posted in Brain Teasers

The Roast with the Most

How do you spell roast?
How do you spell most?
How do you spell coast?
How do you spell post?

What do you put into a toaster?

Bread. (It turns into toast when it’s done toasting).

Posted in Brain Teasers

Three Cuts to Turn a Round Cake Into Eight Equal Slices

How can you cut a round cake three times to make eight equal slices?

Cut #1 – Down the center of the cake (vertically) leaving two equal halves.
Cut #2 – Across the center of the cake (horizontally) leaving four equal slices.
Cut #3 – Through the middle edge of the cake slicing all four of the pieces in equal halves, leaving eight equal slices (four equal tops and four equal bottoms).

Posted in Brain Teasers

Two in a Corner

Two in a corner,
One in a room,
Zero in a house, but one in a shelter.

What am I?

The letter “r”.

Posted in Riddles