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

Sweet or Bitter and Sometimes Free

I often fall from up above,
Sweet or bitter and sometimes free,
Use me to declare your love,
I’m worth more than most any.

An apple. They fall off trees and can be sweet or bitter depending on the type of apple. Most people buy apples, but you can get a free one if you have an apple tree. In olden days apples were used to throw at a person you loved, and in 2013 the company, Apple, pushed past Exxon Mobile to have the largest market capitalization in the United States.

Posted in Riddles

Characters In The Correct Order

Put the characters C D M L X in the correct order (not alphabetical).

X (10), L (50), C (100), D (500), M (1000). They’re Roman numerals in order from smallest to largest.

Posted in Brain Teasers

Born In the Ocean

Born in the ocean,
White as snow,
I’m hidden in water,
Where do I go?

What am I?

Salt. Salt is harvested from seawater, it’s white and it dissolves in water.

Posted in Riddles
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Two Tons

If you had a ton of feathers and a ton of stones which would be heavier?

Neither. A ton is a ton, no matter what it’s made up of, and they both weigh a ton.

Posted in Brain Teasers

After You Wake Up

You do this after you wake up,
And you get all wet,
If you didn’t you would cause,
Those nearby to fret.

What am I?

Getting dressed.

Posted in Riddles
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I Generate Fear But Am Quiet As A Mouse

I can generate fear and some say I come out of your ears. I’m quiet as a mouse but not welcomed in the house.

Smoke.

Posted in Riddles

The Lonely King

King Ferdinand has no immediate living relatives and decides to hold a contest to find a worthy successor when he dies. He gives a seed to every contestant and explains that the person with the healthiest and most beautiful plant will win the throne.

When the final day of the contest arrives, the king finds hundreds of plants of all shapes and sizes. However, he ignores them and awards the throne to a girl holding a pot with only moist dirt.

Why did she win?

King Ferdinand was a kind and trusting man and wanted to be sure he found an honest heir. He gave small pebbles to all the contestants, claiming they were seeds. Therefore, any contestant with a plant had switched their “seed” in order to win. Everyone but the girl had been dishonest.

Posted in Brain Teasers

Two Hours Ago

If two hours ago it was as long after one o’clock in the afternoon as it was before one o’clock in the morning, what time is it right now?

9pm (or 21:00). There are 12 hours between 1pm and 1am, so 6 hours after 1am is halfway. 6 hours + 1pm equals 7pm. In order for 7pm to be 2 hours behind the current time, it must be 9pm.

Posted in Brain Teasers

Fall Crop

What three or four-letter word belongs between the word on the left and the word on the right so that the first and second, and second and third words form a compound word or phrase?

For example: FOOT _ _ _ _ PARK would be BALL, or FOOTBALL and BALL PARK.

1. FALL _ _ _ CROP
2. KNEE _ _ _ SIZE
3. BOARD _ _ _ _ WAY

1. OUT – FALLOUT, OUTCROP
2. CAP – KNEECAP, CAPSIZE
3. WALK – BOARDWALK, WALKWAY

Posted in Brain Teasers