DAY 459

From Reader's Digest
Contributed by L.S. Bowen


Before sailing as a guest on board a submarine, I asked the coxswain if there were any special  regulations to be observed during exercises. I was puzzled when he asked me how good my mental arithmetic was. He went on to explain the golden rule of the submarine service: "Count how many times we dive, add the number of times we surface, divide by two. If there is a remainder of 1, don't open the hatch."

DAY 458

How do you equally divide three oranges among four people?

Answer:

Each person gets 3/4 of an orange. Cut each orange into quarters and give each person three.

DAY 457

Matchstick Puzzle

The equation below in Roman numerals (9-12 = 3) is obviously wrong. Move one line (matchstick) to produce a correct equation. (The solution does not involve an inequality sign, negative numbers, or changing an X to a V.)

IX - XII = III

HINT:
There are 13 lines in the equation.

Answer:

IX = XII - III

DAY 456

From Reader's Digest

If it cost one cent to ride 1,000 miles, how much would a trip around the world cost? How much to go to the moon? The sun? And how much would it cost to go to Alpha Centauri, our nearest star other than the sun. Use the following distances to help solve:


Circumference of the Earth: 25,000 miles
Distance to the moon: 240,000 miles
Distance to the sun: 93,000,000 miles
Distance to Alpha Centauri: 26,000,000,000,000 miles
                                             (26 trillion - 4.2 light years)

Answers:

25 cents to go around the Earth
$2.40 to go to the moon
$930 to go to the sun
$260,000,000 to go to Alpha Centauri

Explanation of the math:

Think of the distances as multiplied by 1,000 - to give the number of cents. Then translate the number of cents into dollars by dividing by 100 (if necessary).

Earth - circumference of 25,000 miles - 25 thousands = 25 cents

Moon - 240,000 miles from Earth - 240 thousands = 240 cents = $2.40

Sun - 93,000,000 miles from Earth - 93,000 thousands = 93,000 cents = $930

Alpha Centauri - 26,000,000,000,000 miles from Earth
                              26,000,000,000 thousands
                              26,000,000,000 cents = $260,000,000 

Note from JA: Alpha Centauri's distance at 26 trillion miles can also be expressed as 4.2 light years. 

DAY 455

What do you get if you divide the circumference of your jack-o-lantern by its diameter?

Answer:

Pumpkin pi

DAY 454

TWENTY-FOUR

Credit: Jon Erickson
HACKING
The Art of Exploitation, 2nd Ed.

Use each of the numbers 1, 3, 4, and 6 once and only once with any of the four math operations to total 24. You may define the order of operations. For example, 3 x (4+6) + 1 = 31 is valid, but incorrect, since it doesn't total 24.
                                                       
[Note from JA: This problem is not nearly as simple as it might appear. You'll appreciate the solution more if you try it first - before looking at the hints or answer.]

HINTS:
1. There are no parentheses, exponents, or radicals in the answer.
2. The answer involves only two math operations.
3. The answer involves fractions.
4. The answer involves division of fractions.

Answer:

[Note from JA: I was able to figure out that the answer had to involve division of fractions. I also figured out that 6 divided by 1/4 would equal 24. But what about that pesky 3? This is where I gave up. Here is the solution:] 

       6 
   1 - 3/4

DAY 453

Credit: Zack Guido
OF COURSE
Presented  by Will Shortz
on NPR Weekend Edition Sunday Puzzle
October 29, 2017

The equation 65 - 43 = 21 is wrong. The answer should be 22. But can you move two numbers in the equation to make a new equation that is correct? The answer remains a straightforward subtraction problem, no symbols are changed or moved, and no parentheses are needed.

Answer:

Move the 3 and the 2 to make them exponents:

65 - 4 (cubed) = 1 (squared) 

65 - 64             = 1