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:

 CurrentFuturePast
Princessx2z(x+y)/2
Princeyxz

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.

xyz
1-10d
-102d
.5.5-1d

It reduced to:

xyz
1004d
0103d
0015d/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

PrincessPrince
43
86
1612
2418
3224
4030
4836
5642
6448
7254
8060

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

Posted in Brain Teasers

Answer This Honestly

What question can you never honestly answer yes to?

Are you asleep? (or dead, or conscious, or being silent).

Posted in Riddles

I Can Create Peace

My first is in alphabet, my third is in Guinness, my sixth is in donut and my eighth is in elephant. My fifth doesn’t appear in walrus, my second isn’t in stealth, but my seventh is in tremendous and my fourth is in horse. I can create peace.

What am I?

Everyone. Several words match the letter requirements, but only everyone satisfies the last statement. The other words are:

absentee
aperture
housetop
evermore

Posted in Riddles

100 Less Than 99

Where do you find that 100 is less than 99?

On a microwave. Most microwaves will run for a minute if you enter 100, but will run for a minute and 39 seconds if you enter 99.

100 is also less than 99 in an ordered ranking, where 1 is first, and 100th is a lower rank than 99th place.

Posted in Brain Teasers

Number Abbreviations

What do these represent?

24 = HiaD
26 = LotA
7 = DotW
9 = LoaC
12 = SotZ
88 = PK

24 hours in a day
26 letters of the alphabet
7 days of the week
9 lives of a cat
12 signs of the Zodiac
88 piano keys

Posted in Brain Teasers

Special Two Letter Combinations

What do these three letter combinations have in common?

DE
HI
MN

Hint: These combinations don’t have it in common.

AK
IN
WY

They are the only three US state abbreviations whose two letters are next to each other in the alphabet.

DE – Delaware
HI – Hawaii
MN – Minnesota

Posted in Brain Teasers

Dumbstruck Beekeeper

Which word does not belong?

beekeeper, dumbbell, dumbstruck, untruthful

Dumbbell. All of the other words have only one of the vowels (a, e, i, o, u).

Posted in Brain Teasers

Bed, Evil, Identical

What word can be added before or after these words to make a new word or phrase?

Bed, Evil, Identical

Twin. Twin bed, Evil twin, Identical twin.

Posted in Riddles

A Seemingly Simple Math Problem

What is the answer to this problem?

1 + 1 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1
1 + 1 × 0 + 1 = ?

30.

There are two tricks to this one. The first is 1 × 0. But it’s mostly there as a distraction. Yes, 1 × 0 is 0, but that doesn’t affect anything else in the equation. The second, far trickier element is that the lines ending with 1 don’t have a + sign next to them. That means they should be combined with the following line.

Let’s put the equation all on one line, shall we?

1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1 × 0 + 1 = ?

And the answer to that equation is 30.

Posted in Brain Teasers

Hangs Others

What hangs others yet can unintentionally hang itself?

A jury.

Posted in Riddles