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True, False or Confused?

Which of the following statements are true and which are false?

1. Only one of the statements is false.
2. Exactly two of the statements are false.
3. Only three of the statements are false.
4. Exactly four of the statements are false.
5. All five of these statements are false.

The only true statement is #4 and the rest are false.

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Turning the Years Upside Down

What years from the 1900s and 1800s are the same year when read upside down?

1961 and 1881.

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The Websters’ Busy Day

Mr. and Mrs. Webster were on a holiday shopping excursion. On their way to the car after leaving the store, Mr. Webster complained he was tired from carrying so many packages. Mrs. Webster, the kindly thing that she was, replied, “Quit your complaining Walter! If you gave me just one of your packages, I’d have twice as many as you. And if I gave you one of mine, we’d have the same.”

How many packages were Mr. and Mrs. Webster each carrying?

Mrs. Webster was carrying 7 packages and poor old Mr. Webster was laden with 5.

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Scrambled Animals

Using each of the letters in this phrase only once, rearrange the letters to make the names of exactly three different animals.

Tall elephant or ape man.

1. Panther
2. Antelope
3. Llama

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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?


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

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