One Two Six Sequence

What is the next number in this series?

1, 2, 6, 42, 1806, ___

To get the next number, multiply the previous number in the series by itself plus one:

n × (n + 1).

For example, to get 6, multiply 2 × (2 + 1)
To get 42 multiply 6 × (6 + 1)

Thus, 1806 × 1807 = 3263442

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The Potato Paradox

Fred brings home 100 pounds of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then leaves them outside overnight so that they consist of 98 percent water. What is their new weight?

50 pounds.

100 lb of potatoes with 99% water weight means there’s 99 lb of water and 1 lb of solids, a 1:99 ratio.

If the water decreases to 98%, then the solids account for 2% of the weight. The 2:98 ratio reduces to 1:49. Since the solids still weigh 1 lb, the water must weigh 49 lb for a total of 50 lbs for the answer.

Read more at the Potato Paradox wikipedia page.

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Six One Seven and Nine to Make Twenty Four

How can the numbers 6, 1, 7 and 9 be arranged to make 24?

91 – 67 = 24
(9 – 6) × (1 + 7) = 3 × 8 = 24

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A Fox and Two Chickens

A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He comes to a river and needs to cross it, he finds a small boat that can carry only him and one animal, how does he get himself, the fox and two chickens across the river safely?

Take the fox over, return with nothing. Go over with one chicken, return with the fox. Go over with the second chicken, return with nothing. Finally, take the fox over.

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What Comes Next I S I T

What comes next in this series?

I S I T P N A A D L I I Y N ___

The letter A.

There are three separate series

1. Starting with the first letter and taking every third letter you get ITALY.
2. Starting with the second letter and taking every third letter you get SPAIN.
3. Starting with the third letter and taking every third letter you get INDIA.

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Captain Mark

Captain Mark is the captain of the ship. The captain of the ship is Captain Mark. The ship has plenty of space.

What is the name of the ship?

The Space Shuttle Endeavour, captained by Mark Kelly.

I received this by email from someone who didn’t know the answer. Thanks to Devon for helping with this answer.

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Only Found In The Past

You will only ever find me in the past. I am created in the present but the future can never taint me. What am I?

History

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A Home But No Family

I have an end but no beginning, a home but no family, a space without room. I never speak but there is no word I cannot make. What am I?

A keyboard.

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An Insect And a Half

I am an insect. Half of my name is another insect. What am I?

Beetle. (Bee is the other insect).

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You Melted My Ice

A full glass of water with a single ice cube sits on a table. When the ice has completely melted, will the level of the water have increased, decreased or remain unchanged?

The water level remains unchanged because the ice cube displaces its own weight. If you’re not convinced, read Archimedes’ Principle, which states that any floating object displaces its own weight of fluid. Still not convinced? Here are a few more sources.

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