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She Was Never There

Emily’s celebration was a success.
Except nobody invited her.

She was at the celebration but was never really there.

How could this be?

Emily passed away and it was a celebration of her life. Of course you don’t invite the deceased. Her body was in the casket, but Emily the person wasn’t there.

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Alfred’s Tough Cash Request

Alfred is at the bank to cash his $200 check. He tells the cashier he would like some one dollar bills, ten times as many two dollar bills and the rest in fives.

How many of each denomination does the cashier need to give Alfred?

Five $1 bills, 50 $2 bills and 19 $5 bills.

We know that in order to give the rest of the amount in fives, the sum of the one and two dollar bills needs to be divisible by five (i.e. end in 0 or 5).

If we start with a single one dollar bill, we’d need ten two dollar bills to satisfy the request, making $21. But we need a sum that is divisible by 5. So we keep going up, like so:

$1 + $2 * 10 = $21
$2 + $2 * 20 = $42
$3 + $2 * 30 = $63
$4 + $2 * 40 = $84
$5 + $2 * 50 = $105 (Aha! It’s divisible by 5)
$6 + $2 * 60 = $126
$7 + $2 * 70 = $147
$8 + $2 * 80 = $168
$9 + $2 * 90 = $189

So the only option that works is 5 $1 bills and 50 $2 bills, leaving $95 (95 / 5 = 19) to be paid out in 19 fives.

Alfred is one tough customer.

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Fill in the Missing Element

Here is a series of numbers:

16 06 68 88 ___ 98

What belongs in the blank spot?

87 is the common answer to this, but it has to be flipped upside down, so I consider L8 more correct.

If you flip the numbers horizontally by 180 degrees:

86 87 88 89 90 91

You see that the blank spot is 87, counting from 86 to 91. However, you need to flip it around, so it becomes L8.

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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.

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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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False Positive HIV Test

Imagine an HIV test that is 95% accurate (false positive rate of 5%) and around 2% of the tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive?

29%

To read more about this, see the False Positive Paradox page on Wikipedia.

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Paula and Quincy

Paula had four times the money that Quincy had, but after Paula gave Quincy $33, Quincy had 3 times as much as Paula.

How much did they each start with?

Paula had $48 and Quincy had $12.

If Q is the amount Quincy had, then 3(4Q – 33) = Q + 33

Solved, Q = 12.

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How to Save Gas

If you could chose to increase the average fuel economy of a car, which of these would save the most fuel?

1. 10mpg -> 12mpg
2. 12mpg -> 15mpg
3. 15mpg -> 20mpg
4. 20mpg -> 30mpg
5. 30mpg -> 60mpg

It turns out they all save the same amount of fuel.

If you travel 100 miles:

100 / 10 = 10 gallons used
100 / 12 = 8 1/3 gallons used

10 – 8 1/3 = 1 2/3 gallons saved

100 / 30 = 3 1/3 gallons used
100 / 60 = 1 2/3 gallons used

3 1/3 – 1 2/3 = 1 2/3 gallons saved

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All Words From Nine Letters to One

What 9-letter word can have a letter removed to make a new word and repeat the process until a single letter remains?

startling
starting
staring
string
sting
sing
sin
in
i

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You’re Halfway There

You’re standing 11 feet away from a doorway and with each step you move halfway to the doorway. How many steps will it take for you to get to the doorway?

Technically, the answer is infinity. If you keep going halfway, you’ll never actually make it to the doorway.

But in practice, after 10 steps you’ll be 1/8th of an inch to the doorway and anyone behind you would say to stop being a baby and take a real step through the doorway already.

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