At Least One is a Boy

A couple has two children. At least one of them is a boy. Assuming the probability of having a boy or girl is 50%, what is the probability that both children are boys?

If you answered 1/2, you’re not without comrades, but the generally accepted answer by statisticians (though not without debate) is 1/3. This is because there are four possible combinations: boy-boy, boy-girl, girl-boy and girl-girl. Since we are told one of the children is a boy (but we don’t know if it’s the first or second child), we can rule out the girl-girl combination, leaving three remaining options. Only one out of 3 is boy-boy, so we get a 1/3 chance.

This is a well-known problem known as the Boy or Girl paradox. The other variation is this brain teaser.

Posted in Brain Teasers

Three Two Three Sequence

What number belongs at the beginning of this sequence?

?, 3, 2, 3, 9, 2, 4, 8, 4, 3, 7, 6

3 ½.

If you break up the numbers into groups of 4, a,b,c,d, then 2 × |a – d| = |b – c|.

9 2 4 8 → 2 × |9 – 8| = |2 – 4|, or 2 × 1 = 2
4 3 7 6 → 2 × |4 – 6| = |3 – 7|, or 2 × 2 = 4, so
n 3 2 3 → 2 × |3 ½ – 3| = |3 – 2|, or 2 × ½ = 1;

I’m not sure this is the correct solution, but it’s the best I’ve found so far. Email me if you know of a better one.

Posted in Brain Teasers
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What’s Nowhere But Everywhere

What’s nowhere but everywhere except where something is?

Nothing. (From Gotham)

Posted in Riddles

A Creature, Part Man

This creature, part man and part tree,
hates the termite as much as the flea.
His tracks do not match,
and his limbs may detach,
but he’s not a strange creature to see.

What is it?

A man with a wooden leg.

Posted in Riddles

Fill in the Missing Element

Here is a series of numbers:

16 06 68 88 ___ 98

What belongs in the blank spot?

87 is the common answer to this, but it has to be flipped upside down, so I consider L8 more correct.

If you flip the numbers horizontally by 180 degrees:

86 87 88 89 90 91

You see that the blank spot is 87, counting from 86 to 91. However, you need to flip it around, so it becomes L8.

Posted in Brain Teasers

Two Plus Two Equals Four

Each letter represents a different digit. Any digit can be used, but zero can never start a word. Given W = 2 and R = 6, what do the rest of the letters represent?

  TWO
+ TWO
------
 FOUR

F = 1
O = 8
R = 6
T = 9
U = 5
W = 2

  928
+ 928
-----
 1856
Posted in Brain Teasers

Sisters and Brothers

My daughter has as many sisters as she has brothers. Each of her brothers has twice as many sisters as brothers. How many sons and daughters do I have?

Four daughters and three sons. Each daughter has 3 sisters and 3 brothers, and each brother has 2 brothers and 4 sisters.

To figure it out mathematically, you could use the following two equations where G = the number of girls and B = the number of boys:
G – 1 = B
2(B – 1) = G

Solving for G gives you 4 and plugging that in to G – 1 = B gives you a B of 3.

Posted in Brain Teasers

Born in 1946, Died in 1947

A man is born in 1946 and dies in 1947, yet he was 86 years old. How is that possible?

He was born in room #1946 of the hospital when he was born, and died in room #1947 86 years later.

Posted in Riddles

What Holds Two People Together?

What holds two people together but touches only one?

A wedding ring.

Posted in Riddles

Three Digits in a Row

On a regular 12-hour digital clock how many times would the same three digits in a row be displayed (e.g. 1:11, 11:12, 12:22) in one day?

34 times. These 17 instances will be visible twice in a 24 hour period.

1:11
2:22
3:33
4:44
5:55
10:00
11:10
11:11
11:12
11:13
11:14
11:15
11:16
11:17
11:18
11:19
12:22

Posted in Brain Teasers