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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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A Monstrosity

I stand tall and am made of steel,
With baguettes and garlic at my heel.

The hunchback’s house could see my head,
I’m more well known than a certain bread.

I love the colors red, white and blue,
But maybe not as much as you.

I’m a marvel for all to see,
Though to some I am a monstrosity.

What am I?

The Eiffel Tower

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I Can Ruin a Lucky Run

I can ruin a lucky run,
Or create an item of wealth,
But for man, woman or child,
I’ll always steal your health.

What am I?

Die. The roll of a die can ruin a game of chance. A die (i.e. mold) is used to create new coins and so far at least, we all die.

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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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Mystical Rock Group

What rock group has four men that don’t sing?

Mount Rushmore.

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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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Important Rebus

What does this represent?

IMPORTANT = IMPORTANT

Equally important.

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An Ancient Invention

What ancient invention allows people to see through walls?

A window.

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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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