Varying Reports

Which statements on this list are true?

Exactly one statement on this list is false.
Exactly two statements on this list are false.
Exactly three statements on this list are false.
Exactly four statements on this list are false.
Exactly five statements on this list are false.
Exactly six statements on this list are false.
Exactly seven statements on this list are false.
Exactly eight statements on this list are false.
Exactly nine statements on this list are false.
Exactly ten statements on this list are false.

	Select Click for Answer
The statements contradict one another, so only one can be true. That means nine are false, so statement 9 is true. Adapted from a problem by David L. Silverman in the Journal of Recreational Mathematics, January 1969.

October 9, 2008January 21, 2013 | Puzzles

Strange Math

Two problems that will make you want to throw a chair at someone, from John Jackson, Rational Amusements for Winter Evenings, 1821:

If from six ye take nine, and from nine ye take ten
(Ye youths, now the mystery explain;)
And if fifty from forty be taken, there then,
Shall just half a dozen remain.

II.

One third of twelve, if you divide,
By just one fifth of seven,
The true result (it has been tried,)
Exactly is eleven.

How? Why?

	Select Click for Answer
I. $strange math solution$ II. One-third of TWELVE is LV, and one-fifth of SEVEN is V. And LV/V = 55/5 = 11. I warned you. See also A Universal Solution.

October 3, 2008January 21, 2013 | Puzzles

War

By Charles Tomlinson. White to play and mate in 4 moves, giving check on every move and forcing Black to do the same.

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1. Nc5+ Kc4+ 2. Bb3+ Rxb3+ 3. axb3+ Qxb3+ 4. Qxb3#

September 23, 2008January 21, 2013 | Puzzles

Lightning Addition

A (probably apocryphal) story tells that, as a 10-year-old schoolboy, Carl Friedrich Gauss was asked to find the sum of the first 100 integers. The tyrannical schoolmaster, who had intended this task to occupy the boy for some time, was astonished when Gauss presented the correct answer, 5050, almost immediately.

How did Gauss find it?

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Gauss included 0 in the series and rearranged the terms into 50 pairs, each of which totals 100: 100 + 0 99 + 1 98 + 2 etc. The 50 pairs together make 5000, which, when added to the unpaired central number, 50, gives 5050, the correct sum.

September 21, 2008January 21, 2013 | Puzzles · Science & Math

There Goes the Neighborhood

A Martian sand lizard can reproduce itself in a single day. Start with a single sand lizard and on succeeding days you’ll have 2, then 4, and so on. In 30 days you’ll have 536,870,912 lizards.

How long would it take to reach that number if you started with two lizards?

	Select Click for Answer
It would take 29 days. Essentially you’d be starting from day 2 in the original example.

September 13, 2008January 21, 2013 | Puzzles

“The Scissors Entangled”

“An old but a capital puzzle.” How can you extricate the scissors from the twine?

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“The scissors may be released by drawing the noose upwards through the eye of the scissors, and passing it completely over them.” From Dick & Fitzgerald, The Book of 500 Curious Puzzles, 1859.

September 8, 2008January 21, 2013 | Puzzles

Steadfast

steadfast chess problem

By W. Bone. White to move and mate in four.

The catch: He must mate with the queen — and she’s glued to the board.

	Select Click for Answer
1. Nd3 Ka3 2. Nb1+ Ka2 3. Kf1 Ka1 4. Nc3# By W. Bone, collected in R.A. Brown, Chess Problems, 1844. (12/12/2008 Thanks to Jason for a three-move solution: 1.Nd3 Ka3 2.Nc4 Ka2 3.Nb4#)

September 4, 2008January 21, 2013 | Puzzles

Measuring the River

measuring the river

A traveler reaches a river at the point A and wishes to know the width across to B. As he has no means of crossing the river, what is the easiest way of finding its width?

From Henry Dudeney.

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“Measure any convenient distance along the bank from A. to C, say 40 yards. Then measure any distance perpendicularly to D, say 12 yards. Now sight along DB and find the point E. You can then measure the distance from A to E, which will here be 24 yards, and from E to C, which will be 16 yards. Now AB:DC = AE:EC, from which it is evident that AB, the width of the river, must be 18 yards.”

August 31, 2008January 21, 2013 | Puzzles

“Cryptic Addition”

cryptic addition

From Henry Ernest Dudeney. Can you prove that this sum is correct?

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“If you turn the page upside down you will find that one, nine, one, and eight added together correctly make nineteen.”

August 19, 2008January 21, 2013 | Puzzles

Fire Escape

You’re new to hell, and you’re given a choice: You can go directly to the fourth circle, or you can play simultaneous chess games against Alexander Alekhine and Aron Nimzowitsch. Alekhine always plays black and smokes a pipe of brimstone. Nimzowitsch plays white and wears cufflinks made of human teeth. Neither has ever lost.

If you can manage even a draw against either player, you’ll be set free. But if they both beat you, you’ll go to the eighth circle for eternity.

What should you do?

	Select Click for Answer
Accept the challenge. Wait for Nimzowitsch’s first move, and then play that move on Alekhine’s board. When Alekhine responds, copy his move on Nimzowitsch’s board. In effect the two masters are playing against one another; you’re just transferring the moves between them. Since their game must end in a win or a draw, you’re guaranteed to escape hell. You don’t even have to know how to play chess!

Click for Answer

August 9, 2008January 21, 2013 | Puzzles