What is the First Number of the Sequence?

If a number in a numeric sequence is 17 and the second number is 3, what is the first number?

I hesitated to add this because it’s poorly worded, ambiguous and the answer could be almost anything. I prefer teasers with a single answer, but there you go.

If you came up with a different answer and can explain how you did it, don’t think you’re wrong. It’s probably just as valid. Feel free to share yours in the comments.

My answer for the first number is 2.

Here’s how I got it.

The generic rule for a number in the sequence is: 2^(n – 1) + 1, where n is the position in the sequence.

Note: The teaser doesn’t specify the position of 17. In this case, it’s fifth.

Position 1: (so n = 1) is 2^(1 – 1) + 1 = 2

Position 2: 2^(2 – 1) + 1 = 3

Position 3: 2^(3 – 1) + 1 = 5

Position 4: 2^(4 – 1) + 1 = 9

Position 5: 2^(5 – 1) + 1 = 17

For the curious, the next 5 numbers of the sequence would be:

Position 6: 2^(6 – 1) + 1 = 33

Position 7: 2^(7 – 1) + 1 = 65

Position 8: 2^(8 – 1) + 1 = 129

Position 9: 2^(9 – 1) + 1 = 257

Position 10: 2^(10 – 1) + 1 = 513

Posted in Brain Teasers

The Man in the Picture

A man is looking at a picture on the wall and says, “Brothers and sisters I have none, but this man’s father is my father’s son.”

What is their relationship?

The man in the picture is the onlooker’s son. Since he doesn’t have any brothers or sisters, the statement my father’s son can only be himself. A shortened version would be this man’s father is me, making him the father of the man in the picture.

Posted in Brain Teasers

Hardware Store Costs

Ralph goes to the hardware store to buy something for his house. He asks the clerk how much one will cost and the clerk looks it up and tells him it will be $3. He asks about buying twelve and is told it will be $6. Two hundred will cost $9.

What is Ralph buying?

Door numbers at $3 each.

Posted in Brain Teasers

Related Strangers

A man gets off the bus looking for an address and approaches a couple walking in the same direction for directions. The woman says they’re going that way and take him. Along the way the man asks if they’re related. The woman grins and says, “We’re not strangers. This man’s mother is my mother’s mother-in-law.” The man is confused but doesn’t say anything. When he gets back home he tells his wife about the conversation and she can’t figure it out either. They decide to ask their lawyer and he eventually works it out with pen and paper. How are the couple related?

The couple is either a man and his daughter or an uncle and his niece.

Posted in Brain Teasers

What Word Could Be Added to Make New Words?

What word could be added to all of these words?

apple
cone
lake
tree
ridge
nuts

Pine.

Posted in Brain Teasers

An Attorney for a Brother

The defendant testified, “The attorney is my brother,” but the attorney took the stand and denied having a brother under oath. Who is lying?

Neither one of them lied. The defendant was the attorney’s sister.

Posted in Brain Teasers

Always Coming But Never Arrives

What is always coming but never arrives?

Tomorrow.

Posted in Riddles

Full of Holes Yet Full of Water

I’m full of holes, yet I’m full of water. What am I?

A sponge.

Posted in Riddles

What Is The Longest Word With Horizontal Symmetry

A word with horizontal symmetry is one whose letters are a mirror image of themselves. If you drew a horizontal line across the word and folded it over, it would overlap on itself. For example, EXCEEDED and ICEBOX have horizontal symmetry, but VERTICAL and SIMPLE do not.

What is the longest word with horizontal symmetry?

CHECKBOOK.

Posted in Brain Teasers

The More You Run

The more you run, the harder I am to catch. What am I?

Your breath.

Posted in Riddles