Three Two Three Sequence

What number belongs at the beginning of this sequence?

?, 3, 2, 3, 9, 2, 4, 8, 4, 3, 7, 6

3 ½.

If you break up the numbers into groups of 4, a,b,c,d, then 2 × |a – d| = |b – c|.

9 2 4 8 → 2 × |9 – 8| = |2 – 4|, or 2 × 1 = 2
4 3 7 6 → 2 × |4 – 6| = |3 – 7|, or 2 × 2 = 4, so
n 3 2 3 → 2 × |3 ½ – 3| = |3 – 2|, or 2 × ½ = 1;

I’m not sure this is the correct solution, but it’s the best I’ve found so far. Email me if you know of a better one.

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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.

Posted in Brain Teasers

A Real Life Emergency

Mary was out riding a frisky pony in a meadow by the sea when the bridle came loose. The animal shook it off and started to gallop full speed toward the ocean, paying no attention to Mary’s yelling to slow down. She couldn’t bear to jump off and lose her beloved pony, so she stayed on and hoped for the best. When the cliff loomed ahead of her, she knew she had to stop the pony. How did she do it?

Mary clapped her hands tightly over the animal’s eyes, causing it to stop.

Posted in Brain Teasers

A Green Ranch

There’s a green ranch house on a green street with green walls, tables and chairs. What color is the staircase?

There is no staircase, it’s a ranch.

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Rearrange My Letters To Be Clean

Rearrange these letters into something you can clean with.

boas

soap (by flipping the b upside down, similar to how IHOP became IHOb)

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Falls But Never Breaks

What falls but never breaks and breaks but never falls?

Night and day.

Posted in Riddles

A Harvest Sown and Reaped

A harvest sown and reaped on the same day
In an unplowed field,
Which increases without growing,
Remains whole though it is eaten
Within and without,
Is useless and yet
The staple of nations.

A war.

Posted in Riddles

Two Hands But Can’t Clap

I have two hands but I cannot clap. What am I?

A clock.

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Turns Everything Around

What turns everything around but doesn’t move?

A mirror.

Posted in Riddles

Long Legs Crooked Thighs

Long legs, crooked thighs,
Little head and no eyes.
No burn, make a ting,
Use hands, but no ring.

What am I?

A pair of tongs.

Posted in Riddles