I Start Out The Same As Others

I start out the same as others,
Then grow to four legs and four arms,
And two hearts beat inside,
Until the separation.

What am I?

A pregnant woman is like other women, then the baby forms, and then is delivered.

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Four Gallons From Two Buckets

You have two buckets. One holds exactly five gallons and the other three gallons. How can you measure exactly four gallons of water into the five gallon bucket?

Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.

  1. Fill the 3-gallon bucket.
  2. Pour the 3 gallons of water into the 5-gallon bucket
  3. Fill the 3-gallon bucket again.
  4. Fill up the 5-gallon bucket with the 3-gallon bucket, leaving you with 1 gallon left in the 3-gallon bucket.
  5. Empty out the 5-gallon bucket.
  6. Pour the remaining 1 gallon of water from the 3-gallon bucket into the 5-gallon bucket.
  7. Fill the 3-gallon bucket.
  8. Pour the 3 gallons of water from the 3-gallon bucket into the 5-gallon bucket leaving you with 4 gallons of water in the 5-gallon bucket.

Alternate solution:

  1. Fill up the 5 gallon bucket
  2. Pour it into 3 gallon bucket, leaving 2 gallons
  3. Empty out the 3 gallon bucket
  4. Pour the 2 gallons in the 5 gallon bucket into the 3 gallon bucket
  5. Fill up the 5 gallon bucket and pour it into the 3 gallon bucket until it’s full, leaving 4 gallons in the 5 gallon bucket.
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Always Old, Sometimes New

Always old, sometimes new.
Never sad, sometimes blue.
Never empty, sometimes full.
Never pushes, always pulls.

What am I?

The moon. The moon has been around for quite some time, but there’s a “new” moon every month or so. A Blue moon is a rare event. The moon is a body of rock, so it’s never empty, but we do see what we call a full moon some nights. And the moon’s gravity “pulls” on the ocean to create low and high tides, but it doesn’t push anyone around because it’s a friendly fellah.

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Largest Product

Using all the digits from 1 to 7, what two numbers have the largest product? For example, 1234 x 567 = 699678 but you can do much better than that.

742 x 6531 = 4,846,002.

A similar problem can be found in L.A. Graham’s Ingenious Mathematical Problems and Methods with a range of 1 to 9, but the principle remains the same – the numbers with the smallest difference produce the largest product. You start out with the highest two digits, 7 and 6, then attach 5 and 4, putting the smaller of the two digits with the larger number, giving you 74 and 65. The next two highest digits are 3 and 2, giving you 742 and 653. Finally, you add the 1 to the lower number. Page 80 has the details of that solution.

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I Can Always Go Up, Never Down

I can always go up, never down,
I can always turn left, never right,
I am always hot when I’m cold

A ski lift.

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Mother From a Family of Eight

This mother comes from a family of eight,
Supports her children in spite of their weight,
Turns around without being called,
Has held you since the time you crawled.

Who is she?

“Mother” Earth. The family of eight are the eight planets, all of the world’s population is quite a load, the earth is always spinning (or turning around) and unless you’re an alien, you’ve been on earth your whole life.

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My First Wears My Second

My first wears my second; my third might be
What my first would acquire if he went to the sea.
Put together my one, two, three
And the belle of New York is the girl for me.

Manhattan. A MAN wears a HAT, and a MAN might acquire a TAN if he went to sea.

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I Have Wings But Cannot Fly

I have wings but cannot fly.
I can do the twist but can’t move around.
People enjoy relaxing in my company.

What am I?

A ceiling fan.

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Four Nines To Make a Hundred

How can you make four 9’s equal 100?

99 9/9 = 100

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The Average of Three

There are three numbers. The first two are 2/3 and 3/4.

What does the third number have to be to make the average of all three be 2?

4 7/12

In order for the average of three numbers to be 2, they must all add up to 6. That gives you this equation:
2/3 + 3/4 + n = 6

Solve for n = 55/12, or 4 7/12.

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