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

Tongue Can’t Taste, Throat Can’t Swallow

What has a tongue that can’t taste, a throat that can’t swallow, eyes that can’t see and a soul that will never die?

A shoe. It has a tongue, a throat, eyes (or eyelets) and a sole. I used soul here or else it would have given the answer away, but this riddle works best when told rather than read. And as the joke goes, old shoes never die, they just lose their sole.

Posted in Riddles

No Head On Which A Hat To Place

I always run but never walk,
I sometimes sing but cannot talk,
No head on which a hat to place,
You always look me in the face.

What am I?

A clock. It runs all the time, it “sings” for hourly chimes, cuckoos or alarms, it doesn’t have a head (but does have hands) and you look a clock in the face to tell the time.

Posted in Riddles

Everybody Does At The Same Time

What is it that everybody does at the same time?

Grow older.

Posted in Riddles

Teams Assembling Bikes

If 6 bike makers can assemble 9 bikes in a day and a half, how many of them would it take to assemble 270 bikes in 30 days?

9. Each bike maker can assemble one bike a day.

Posted in Brain Teasers

Priscilla and Bruce Exchanging Money

Priscilla gave her brother Bruce as much money as Bruce started with. Bruce gave Priscilla as much money as Priscilla had left. Priscilla then gave Bruce as much as Bruce had left, which left Priscilla broke. Bruce had $80.00.

How much money did Priscilla and Bruce start with?

Priscilla: $50
Bruce: $30

Step 1
Priscilla gives Bruce $30
Priscilla: $20
Bruce: $60

Step 2
Bruce gives Priscilla $20
Priscilla: $40
Bruce: $40

Step 3
Priscilla gives Bruce $40
Priscilla: $0
Bruce: $80

Posted in Brain Teasers

A Fox, Chicken and Sack of Grain

You have a fox, a chicken and a sack of grain. You must cross a river with only one of them at a time. If you leave the fox with the chicken he will eat it; if you leave the chicken with the grain he will eat it. How can you get all three across safely?

Fox and (little) chicken

Take the chicken over first. Go back and bring the grain next, but instead of leaving the chicken with the grain, come back with the chicken. Leave the chicken on the first side and take the fox with you. Leave it on the other side with the grain. Finally, go back over and get the chicken and bring it over.

Posted in Brain Teasers

A Wonderful Help To Women

I am a wonderful help to women,
The hope of something to come.
I harm no citizen except my slayer.
Rooted I stand on a high bed. I am shaggy below.
Sometimes the beautiful peasant’s daughter, an eager-armed,
Proud woman grabs my body,
Rushes my red skin, holds me hard,
Claims my head. The curly-haired
Woman who catches me fast will feel
Our meeting. Her eye will be wet.

What am I?

An onion. Onions help add flavor to meals, they make the person who cuts them cry and they grow hair downtown.

Posted in Riddles

Instrument Can’t Be Touched Nor Seen

What instrument can make any sound and be heard but not touched or seen?

Your voice.

Posted in Riddles

What Digit Does Each Letter Represent?

This is what you know:

1. Each letter represents a different digit from 1 to 9
2. The total of each row is 17.
3. (B × B) + B + F = A
4. C × F = EF (a 2-digit number, not their product)

A B C
D E F

What digit does each letter represent?

A = 7
B = 1
C = 9

D = 8
E = 4
F = 5

A + B + C = 17
D + E + F = 17
B2 + B + F = A
C × F = EF

To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.

2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.

C × F = EF
9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.

Posted in Brain Teasers