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

B C D

B, C, D, E, G, P

What is the next letter in the sequence?

T. All of the letters rhyme.

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Amber Knits and Fauna Worry

Find a single letter that replaces the first letter in the two words of each row to make two new words. What word is formed by combining the new letter of each row?

For example: PLANK _ BRISK

The new letter is F, making FLANK and FRISK. And F would be the first letter of the answer.

AMBER _ KNITS
FAUNA _ WORRY
WARNS _ AERIE
FEMUR _ GAILY

1. U – UMBER and UNITS
2. S – SAUNA and SORRY
3. E – EARNS and EERIE
4. D – DEMUR and DAILY

The new word is USED.

Posted in Brain Teasers

Five Hundred Begins It

Five hundred begins it, five hundred ends it,
Five in the middle is seen;
First of all figures, the first of all letters,
Take up their stations between.
Join all together, and then you will bring
Before you the name of an eminent king.

DAVID (Roman numerals).

Posted in Riddles

The Answer Isn’t 6

What goes in place of the question mark?

1 3 5
2 4 ?

(It’s not 6)

R. It’s a representation of a stick shift, where 1-5 are gears and R represents reverse.

Posted in Brain Teasers

How to Escape?

A man is trapped in a room with only two possible exits. Through the first door is a room with an enormous magnifying glass causing the blazing hot sun to instantly burn anything that enters. Through the second door there is a fire-breathing dragon. How does the man escape?

Leave through the first door at night when the sun is down.

Posted in Brain Teasers

Harvest Though No Grain

I harvest you, though you’ve no grain,
I reap you in the wind and rain,
You bleed not but your soft meat
And nectar makes a sweetest treat.
What am I?

A clam or oyster. You harvest clams or oysters on the beach or go diving, and the beach is often windy and rainy. Neither bleeds but are known for having, soft, slimy meat, and people often drink the “clam nectar” or “oyster juice”.

Thanks to Helena for this submission

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The Honest and Dishonest Guards

You’re in a room with two doors. There’s a guard at each door. One door is the exit, but behind the other door is something that will kill you. You’re told that one guard always tells the truth and the other guard always lies. You don’t know which guard is which. You are allowed to ask one question to either of the guards to determine which door is the exit.

What question should you ask?

Ask either guard what door the other guard would say is the exit, then choose the opposite door.

If you ask the guard who always tells the truth, he knows the other guard would lie, so he’ll point you to the door leading to death. If you ask the guard who always lies, he knows the other guard would truthfully show you the exit, so he’ll lie and point you to the door leading to death.

An alternate solution is to ask a guard what they would answer if you were to ask them which door was the exit, then choose that door. The truthful guard will point to the correct exit, but the lying guard will too. Here’s why. If you asked him what door was the exit, he would normally lie and point to the death door, but you asked him what he would say if you asked what door was the exit, and in order to lie to that question, he will point you to the exit.

Posted in Brain Teasers

From Scraps to Pants

A tailor can make a pair of pants from the scraps left over from sewing up five pairs of pants. If he has twenty-five scraps, how many pairs of pants can he make?

Six pairs of pants. He can make five initially, but once he’s done making five pairs of pants, he’ll have five remaining sets of scraps, meaning he can make an additional pair of pants, totaling six.

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Falling Window Cleaner

A window cleaner is cleaning a window on the 25th floor of a skyscraper when he slips and falls. He has no safety equipment and nothing to soften his fall, yet he is not hurt. How can this be?

He was cleaning the inside of the window.

Posted in Brain Teasers