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Logic Puzzles

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Problems, puzzles and peculiarities 		Logic puzzles and problems


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Introduction

This is a motley selection of logic puzzles and similar brain-tormenting problems. Some of them are as old as the hills whilst others are original. The solutions are there to be had if you're completely stuck, or if you just want to see if your answer is better than mine. I've tried to arrange the solutions so that you won't accidently see the answer to nearby problems whilst looking at them.


The Puzzles

Three utilities

Three utilities

Three utility companies (electricity, water and gas) are to put in underground supplies to three houses. Each of the companies is to put in one pipe or cable to each of the three houses, but they have an agreement that none of their pipes or cables can be laid in such a way as to be buried above any of the others, whether running along the same line or crossing. All pipes and cables must be buried along their entire lengths. How can this be done?

Solution


Knights and Knaves 1

There are many problems of this sort: the setting is an island where some of the inhabitants always tell the truth, and the others always lie. The truthtellers are known as knights, and the liars as knaves.
How, with just one question, can you establish for certain whether an inhabitant of the island is a knight or a knave?

Solution


The block

A man is standing on a large solid flat-topped block. In front of him on the block are two chairs. In one chair a man is sitting, and in the other a woman. Their heads are cut cleanly across, and the tops are hinged back like lids. The standing man has his left hand inside the woman's head, and his right hand inside the man's. A well-known expression describes what is happening. What is it? (If you don't want a clue, read no further).

.

.

.

Here's the clue, for what it's worth. What is the block made of? (And yes, you do have enough information to establish that!).

Solution


Two iron bars

You are in a windowless brick-walled cell; the thick wooden door is barred on the outside. Your clothes contain no metal of any kind. There is no metal in the cell, except for two iron cylinders. One is a bar magnet, the other is not. How can you determine which is which? You are only permitted to touch them together once.

Solution


Matches

MatchesMove two and only two matches to reduce the number of unit squares from five to four. Matches may not be crossed. They may only be moved to new positions, not taken away. Every match must be part of at least one unit square.

Solution


"Now, I know..."

What is the purpose of the following sentence?

Now, I know a super utterance to assist maths

Solution


Black King

This is one of Sam Loyd's problems:

1: Place the black king where he would be stalemated

2: Place the black king where he would be checkmated

3: Place the black king where he would be checkmated next move

4: Place the black king where he can never be checkmated

White: Kc3 Qg4 Bg1

Solution


One hundred

Connect the digits 1 to 9, in numerical order, using any or all of the four main operational signs (+ - × ÷) and brackets, to make a total of one hundred. (e.g. 1 + 23 × 4 ...etc... = 100)
There are many solutions.

Solution


Two balls in space

You are floating weightless in space. Beside you are floating two apparently identical lead spheres, each about one foot (thirty centimetres) in diameter. You know that one is a solid lead sphere, and the other is a hollow lead shell. How can you tell which is which?

Solution


More matches

7> matches forming V I = I IMove one and only one match to give a valid equation. The match may not be taken away, and crossed matches are not allowed. There are at least two answers.

Solution


A little light verse

Explain the following:

Singers honour six, Ben,
Spock, it's full, your eye;
"Foreign twin to blackbird",
Spake Tinner Pye.

Solution


Odd ones out

Which is the odd one out in each of the following lists?

1: 17 37 57 277 797

2: Bats Ewe Lamba Rats Tigre

3: large drive static phonic handy

Solution


The extra square

The extra square

If you draw the square and the lines within it carefully on graph paper, then cut out the shapes, you will find that they can be reassembled to form the rectangle. However, the area of the square is 21x21=441, but the area of the rectangle is 34x13=442. Where has the extra unit square come from?

Solution


How old?

Hannah is just ten years old. Her brother Allen is nearly sixteen. Their father, Uri, is forty, and their mother, Loretta, is thirty-five. How old is their aunt Melissa?

Solution


Still more matches

Move one and only one match to make a square. The match may not be taken away, and crossed matches are not allowed.4 vert. and 1 hor. to form a capital H

Solution


Date change

When does Oct 31 equal Dec 25?

Solution


The portrait

A man is looking at a portrait. He is asked, "Whose picture are you looking at?" He replies, "Brothers and sisters have I none, but this man's father is my father's son."
Whose picture is he looking at?

Solution


Pentominoes

A pentominoTake 5 unit squares. Arrange them so that each square aligns at least one edge with an edge of at least one other square. The result is a pentomino. There are twelve unique pentominoes, not counting mirror images. One is shown, left.
Pentominoes can be fitted together like pieces in a jigsaw puzzle, to form rectangular blocks of 6x10, 5x12, 4x15 and 3x20 unit squares. On the right is one of the many 6x10 blocks. The pieces are given letter names for easy reference, based on their resemblance (close or not so close) to certain letters - FLIP STUVWXYZ (S is sometimes called N). Some pieces have mirror images that are enantiomorphs. These are not counted as separate pieces, but pieces can be used either way up.A 6 x 10 matrix


The problem here is to find a solution to the 3x20 block, or in other words to find a way in which the twelve pentominoes can be fitted together to make a perfect rectangle 3 squares by 20 squares. There are two solutions, and as each has a mirror image it could be said that there are four solutions. Some pentominoes are essentially different when picked up and turned over: they can be used either way up.

Solution


Knights and Knaves 2


Another problem set on that island where every inhabitant is either a knight who always tells the truth, or a knave who always lies.
On the island you encounter three inhabitants standing together. Let us imaginatively call them A, B, and C. You ask A, "Are you a knight or a knave?" He replies, but not quite catching his answer, you then ask B, "What did A say?" B replies, "A said that he is a knave." C then says, "Don't listen to B, he's lying."
Can you determine from this whether A is a knight or a knave? If so, which? And what about B? And C?

Solution


Something entirely different

And now for something entirely different... This one has no set solution, but is more of a thought experiment. What would be different if the earth's direction of rotation on its own axis was (and always had been) the opposite of what it is?

Solution



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