I Can Sound a Gong

I’m in bowling and baseball,
For better or for worse,
On a match (but not the sporting kind),
I can sound a gong,
And I’m gone.

What am I?

Strike.

A strike in bowling is good. In baseball it’s good for the pitcher but not for the batter. You can strike a match to light it. When the clock strikes one a gong sounds and when you strike a paragraph, it’s gone.

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An Insect And a Half

I am an insect. Half of my name is another insect. What am I?

Beetle. (Bee is the other insect).

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A Special Something Shared

The numbers 3, 7, 8, 40, 50 and 60 all share something that no other whole number does. What is it?

When spelled out in English they each have exactly five letters.

Posted in Brain Teasers

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.

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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.

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Hangs Others

What hangs others yet can unintentionally hang itself?

A jury.

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Fifty Quarters

You have fifty quarters on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < x < 50. You are asked to separate the coins into two piles in such a way that the number of heads up coins in both piles is the same at the end. You may flip any coin over as many times as you want.

How can you do it?

Take x coins, flip all of them and put them in one pile. The rest of the coins form the second pile.

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Pronounced As One Letter, Written With Three

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I’m double, I’m single,
I’m black, blue, and gray,
I’m read from both ends,
And the same either way.

What am I?

Eye. It’s pronounced like the letter ‘i’, but written with three letters. There are only two letters used (‘e’ and ‘y’). The eye is double with two ‘e’s and represents a single eye. The eye is made up of various colors, some of which are black, blue and gray. And lastly, the eye is a palindrome, spelled the same forward and backward.

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What Can You Break But Not Touch?

What can you break but not touch?

A promise.

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As Long As They’re Dead

This is a place. The first letter is after A and before Z but nowhere in between. You can bring as many people as you want, as long as they’re all dead. Where is it?

The cemetery. The letter C is after A and before Z, and it’s not found in the word “between”. The cemetery won’t take live ones. Fortunately I don’t speak from experience on that.

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