Royal Pain

You’re a knight in love with a princess. Unfortunately, the king knows you’re poor and disapproves of the match.

On the night of a great feast, the king calls you up before his men and presents a golden box. In it are two folded slips of paper. One, he announces, reads “Marriage,” the other “Death.” “Choose one,” he says.

Pretending to stir the fire, the princess manages to whisper that both slips say “Death.” But the king and his men are waiting, and you cannot escape now.

What should you do?

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Rock and Roll

Worshipful natives are rolling a giant statue of me across their island. The statue rests on a slab, which rests on rollers that have a circumference of 1 meter each. How far forward will the slab have moved when the rollers have made 1 revolution?

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“Christopher Crusty’s Little Idea”

http://books.google.com/books?rview=1&pg=PA103&id=5m4ZAAAAYAAJ#PPA102,M1

White to mate on the move.

“A real-right-down regular rare one. The problem exhibited is quite correct Chess, and no violation of any law takes place. In fact, it is found to be quite easy — when you know how.”

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Two by Two

Here’s a curious way to multiply two numbers. Suppose we want to multiply 97 by 23. Write each at the head of a column. Now halve the first number successively, discarding remainders, until you reach 1, and double the second number correspondingly in its own column:

two by two - first image

Cross out each row that has an even number in the left column, and add the numbers that remain in the second column:

two by two - second image

That gives the right answer (97 × 23 = 2231). Why does it work?

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“Paradox, by a Lady”

One summer evening, as I was walking in the fields, I heard somebody behind me calling out my name. I turned round, and saw a friend of mine, at the distance of 400 yards, approaching to join me. We each of us moved 200 yards, with our faces towards the other, in a direct line yet we were still 400 yards asunder. How could this be?

The Nic-Nac; or, Oracle of Knowledge, Sept. 13, 1823

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Trade Relations

Northland and Southland were happy neighbors until yesterday, when Northland declared that a Southland dollar was to be worth only 90 Northland cents.

Not to be outdone, Southland declared that a Northland dollar would be worth 90 Southland cents.

I live in Centerville, on the border between the two countries. I go into a Northland store and buy a kazoo, which costs 10 cents. I pay for it with a Northland dollar and receive a Southland dollar as change.

Then I go across the street and enter a Southland store. There I buy a lemon, which also costs 10 cents. I pay for it with a Southland dollar and receive a Northland dollar as change.

When I get home I have my kazoo and lemon, for which it appears I’ve paid nothing. And each of the merchants has an additional 10 cents in his receipts.

So who paid for the kazoo and the lemon?

(From Eugene Northrop.)

“An Ingenious Match Puzzle”

From Henry Dudeney:

dudeney match puzzle

“Place six matches as shown, and then shift one match without touching the others so that the new arrangement shall represent an arithmetical fraction equal to 1. The match forming the horizontal fraction bar must not be the one moved.”

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Figure and Ground

An island is a body of land surrounded by water, and a lake is a body of water surrounded by land.

Now suppose the northern hemisphere were all land, and the southern hemisphere water. Is one an island, or is the other a lake?