Wily Winifred and the Case of the Odd Numbers

Mrs. Shine was having a rough day and wanted a break. So she asked her class to calculate the sum of the first 50 odd numbers. In a few moments, Winifred was at her desk with the correct answer of 2,500. Stunned, Mrs. Shine figured she must have gotten lucky, and sent precocious Winifred back to her seat with the task of finding the sum of the first 75 odd numbers. Again, Winifred returned in seconds with the correct answer (5,625).

How did Winifred find the answer so quickly?

Winifred, being the precocious child she is, realized there was a pattern when computing smaller sums of odd numbers.

First 3: 1 + 3 + 5 = 9
First 4: 1 + 3 + 5 + 7 = 16
First 5: 1 + 3 + 5 + 7 + 9 = 25

Do you see the pattern like our dear friend Winnie?

For the first n odd numbers, the sum is equal to n2. Thus the first 50 is 502, or 2,500, and the first 75 is 752, or 5,625.

Posted in Brain Teasers

Jim’s Canoeing Adventure

Jim was canoeing on a lake when a sudden thunderstorm blew in tipped his boat. He swam to a rocky island about a mile from his family’s cottage and found a small, abandoned shack. Inside was an old kerosene lamp and a few matches. All the wood on the island was too damp to burn and the lamp was his only means of signaling for help but it only held an inch of kerosene, not enough to reach its short wick. How did he get the lamp burning to summon help?

Knowing kerosene and water wouldn’t mix and kerosene is less dense than water, he dipped the lamp in the lake and filled it with enough water so the kerosene rose to the top to cover the wick. The lamp was still burning an hour later when a motorboat rescued him.

Posted in Brain Teasers

Four Letters and a Fruit or Vegetable

I have four letters in my name,
I am a fruit or a vegetable,
I look like a giant green onion,
I end with the letter k.

What am I?

The leek. It has four letters, has been considered both a fruit and a vegetable, looks like a green onion and ends with the letter k.

Posted in Riddles

I Go Around In Circles

I go around in circles,
But always straight ahead
Never complain,
No matter where I am led.

A wheel.

Posted in Riddles

Dirty Rebus

What does this represent?

    D
    I
D I R T Y
    T
    Y

Dirty double crosser. (Thanks to Ian for the answer)

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If You Have Three, You Have Three

If you have three, you have three.
If you have two, you have two.
But if you have one, you have none.

What am I?

Choices.

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Favorite Use Is Attached To A String

A three-letter word I’m sure you know,
I can be on a boat or a sleigh in the snow,
I’m pals with the rain and honor a king,
But my favorite use is attached to a string.

What am I?

A bow. It has three letters, the bow of a boat is the front, bows are found on the presents on Santa’s sleigh, rainbows come with the rain, one bows before a king and a bow and arrow requires a string.

Posted in Riddles

In A Dark Room with a Rope and a Pencil

Imagine you are in a dark room with a locked door. All you have with you is a rope and a pencil. You can hear the rain outside, but there
are no windows. How do you get out?

Stop imagining.

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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

Thought Rebus

What does this represent?

          but
thought thought

But on second thought.

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