Plep's Puzzles

2008-01-02T16:37:00.000-08:00

One day a girl celebrated her birthday. Two days later, her older twin brother celebrated his. How is this possible?

2007-12-22T17:49:00.000-08:00

A young woman in Manhattan has two boyfriends - one in the Bronx and one in Brooklyn - both of whom she likes equally well.
To visit the boyfriend in the Bronx she takes the subway from the uptown side of the platform; to visit the boyfriend in Brooklyn she takes the subway from the downtown side of the same platform.
As she likes them both equally well, she simply takes the first train that comes along. Brooklyn and Bronx trains run equally often from this platform - every ten minutes - and are equally reliable. Yet for some reason she finds herself visiting the boyfriend in Brooklyn nine times out of ten. Why?

2007-12-21T13:33:00.000-08:00

1/ Make 24 out of 1, 5, 5, and 5.
2/ Make 24 out of 3, 3, 8 and 8.

2007-12-13T19:46:00.000-08:00

You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled -- one says "apples," one says "oranges," and one says "apples and oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?

2007-12-06T17:41:00.000-08:00

1/ Make 4 out of 2,5,6 and 8.

2/ Make 40 out of 4,6,8 and 8.

2007-11-29T13:58:00.001-08:00

A family party included the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But there were not as many people in attendance as it sounds. How many were there, and who were they?

2007-11-23T09:35:00.000-08:00

1/ Make 33 out of 1,2,6 and 7.
2/ Make 34 out of 1,2,6 and 7.

2007-11-17T16:46:00.001-08:00

1/ Make 17 out of 1,2,6 and 7.
2/ Make 32 out of 1,2,6 and 7.

2007-11-14T13:24:00.000-08:00

There are 3 bags. One contains 2 gold coins, another has 2 silver coins and the 3rd has one of each.
You pick a bag at random, and without looking inside take out one coin. It's gold. What is the probability that the other coin in that bag is also gold?

2007-11-05T10:30:00.000-08:00

Combining the digits 1,2,7 and 8, form the integers from 1 to 10.
This is possible with the basic operations +, -, * and / .

Pouring Puzzle

2007-10-11T12:52:00.001-07:00

You have access to a 5 litre bowl, a 3 litre bowl, a working water tap, and a drain.
How could you measure out exactly 4 litres of water?

2007-10-04T04:14:00.001-07:00

Nora has always been 45 years older than Sid, but now the two digits in Nora's age, both prime, are the reverse of the two in Sid's age. How old is Nora?

2007-09-28T04:19:00.001-07:00

When Sid Bloggs was murdered, in a rather compromising position, the detective suspected Sid's wife Nora. Nora however, steadfastly maintained that on the evening of the murder she was in a restaurant with a male friend.
The detective had found an entry in Nora's diary for that evening which apparently confirmed her alibi as follows :
TIPS THE BRUSHED CHEFS. However, the detective realised that the message was coded, and that each letter could be moved either one place forwards or one place backwards in the alphabet to reveal a startling confession. What was the hidden confession?

2007-09-21T15:03:00.001-07:00

A man lives on the twelfth floor of an apartment building. Every morning he takes the lift down to the lobby and leaves the building. In the evening, he gets into the lift, and, if there is someone else in the elevator he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment. Why?

2007-09-18T14:05:00.001-07:00

MOSCOW=1100. LONDON = 550. TEL AVIV = 61. PARIS = 1. BERLIN = ?

2007-09-08T09:58:00.000-07:00

1/ Anastasia, Brenda and Cornelia toss a fair coin 15, 16, and 17 times respectively. Which one is least likely to have tossed more heads than tails?
2/ The same, except the coins are tossed 18, 19, and 20 times respectively?

2007-09-01T23:00:00.000-07:00

A commuter falls asleep on a train halfway to her destination. She slept until she had half as far to go as she went while she slept. How much of the whole trip was she sleeping?

Lunars

2007-08-25T10:47:00.000-07:00

H.G. Wells's novel 'The First Men in the Moon' features intelligent insect-like beings who live in caverns below the surface.
Let us assume that these creatures have a unit of distance called a 'lunar'. It was adopted because the Moon's surface area, expressed in square lunars, exactly equals the Moon's volume, expressed in cubic lunars.
The Moon's diameter is 2160 miles.
How many miles long is one lunar?
(For the purposes of this puzzle, you may assume that the Moon is a perfect sphere).

2007-08-18T13:04:00.000-07:00

Express 100 with five 1's.

Express 100 at least three ways with five 5's.

(I've found seven ways of doing this so far - I'm sure there are more).

Four 4's - next part

2007-08-11T23:34:00.000-07:00

Using arithmetic operations, express the integers from 31 to 50.
You are allowed the standard arithmetic operations, including +, -, *, /, and square root (e.g. sqrt(4)).
The following operations may be useful :
Concatenation. 44 is valid as part of an answer.
Decimals. 4.4 is valid as part of an answer; so is .4 .
Recurring decimals. E.g. .4r (or .4recurring) is the same as .444... - or 4/9 - and valid.
Factorials. The factorial of a positive integer (written as n!) is the product of all the positive integers less than or equal to that number. E.g. 4! = 4*3*2*1 = 24.
Double factorials. The double factorial of an even positive integer (written as n!!) is the product of all the positive even integers less than or equal to that number. The double factorial of an odd positive integer is the product of all the positive odd integers less than or equal to that number. E.g. 4!! = 4 * 2 = 8, and 5!! = 5 * 3 * 1 = 15.
Powers. 4^4 means 4 to the power of 4, and 4^sqrt(4) means 4 squared (or 16). You don't actually need these for these numbers, but you can use them if you like.
Don't use operations like cube roots and inverses (e.g. 1/4). The reason for this is that in normal notation, these use numbers other than 4.

The following may also be useful :
n = sqrt(n) * sqrt(n), n being any number
0 = n-n
1 = n/n (unless n is 0)
2 = (n+n)/n
3 = (n+n+n)/n
10 = 4/.4
5 = sqrt(4)/.4
9 = 4/.4r
3 = sqrt(4/.4r)

2007-08-05T03:54:00.000-07:00

Take the sequence of numbers 123456789.
Place + and - symbols between the numbers so that you get a sum of 100.

Four 5's

2007-07-30T09:51:00.001-07:00

Using arithmetic combinations of four 5's express the integers from 1 to 12.
You must use all four 5's for each integer.
You may combine the 5's using the arithmetic operations +, -, * (multiplication) and / (division).
You are also allowed to use sqrt (square root) (e.g. sqrt(5) ).
You are allowed to use concatenation (e.g. 55 is valid as part of an answer).
You are allowed to use decimals (e.g. 5.5 is valid as part of an answer; so is .5).
You are allowed to use factorials. For example, 5! (or factorial(5)) = 5*4*3*2*1 = 120.
(The factorial of an integer x! is the product of all the positive integers less than or equal to x).
You do not need to use anything other than those listed above - so no powers of 3, trig operations, logarithms, cube/quartic/etc. roots, etc.

Four 3's

2007-07-21T03:51:00.000-07:00

Using arithmetic combinations of four 3's express the integers from 1 to 15.
You must use all four 3's for each integer.
You may combine the 3's using the arithmetic operations +, -, * (multiplication) and / (division).
You are also allowed to use sqrt (square root) (e.g. sqrt(3) ).
You are allowed to use concatenation (e.g. 33 is valid as part of an answer).
You are allowed to use factorials. For example, 3! (or factorial(3)) = 3*2*1 = 6. (The factorial of an integer x! is the product of all the positive integers less than or equal to x).
You do not need to use anything other than those listed above - so no decimal places, powers of 3, trig operations, logarithms, cube/quartic/etc. roots, etc.

Four 4's Part 3

2007-07-14T00:00:00.000-07:00

Using arithmetic combinations of four 4's express the integers from 21 to 30.
You must use all four 4's for each number.
You may combine the 4's using the arithmetic operations +, -, * (multiplication) and / (division).
You are also allowed to use sqrt (square root) (e.g. sqrt(4) ).
You are allowed to use concatenation (e.g. 44 is valid as part of an answer).
You are allowed to use factorials. For example, 4! (or factorial(4)) = 4*3*2*1 = 24.
(The factorial of an integer x! is the product of all the positive integers less than or equal to x).
You do not need to use anything more exotic than those listed above - so no decimal places, powers of 4, trig operations, logarithms, cube/quartic/etc. roots, etc.

Four 4's Part 2

2007-07-05T10:35:00.000-07:00

Using arithmetic combinations of four 4's express the integers from 11 to 20.
You must use all four 4's for each number.
You may combine the 4's using the arithmetic operations +, -, * (multiplication) and / (division).
You are also allowed to use sqrt (square root) (e.g. sqrt(4) ). Y
ou are allowed to use concatenation (e.g. 44 is valid as part of an answer).
You are allowed to use factorials. For example, 4! (or factorial(4)) = 4*3*2*1 = 24. (The factorial of an integer x! is the product of all the positive integers less than or equal to x).
You do not need to use anything more exotic than those listed above - so no decimal places, powers of 4, trig operations, logarithms, cube/quartic/etc. roots, etc.

Four 4's

2007-06-29T09:11:00.000-07:00

Using arithmetic combinations of four 4's express the numbers from 1 to 10.
You must use all four 4's for each number.
You may combine the 4's using the arithmetic operations +, -, * (multiplication) and / (division).
You are also allowed to use sqrt (square root) (e.g. sqrt(4)=2, sqrt(4/4)=1).
You do not need to use concatenation (e.g. 44), decimal places (e.g. 4.4), factorials (e.g. 4!), or trig functions such as sin or cos.

2007-06-20T04:03:00.000-07:00

CM is good, MC is bad.
C is good, M is bad.
IX is good, XI is bad.
L is bad, I is good.
Why?

2007-06-09T04:58:00.001-07:00

1/Make 4 out of 2,5,6, and 8.

2/Make 40 out of 4,6,8, and 8.

2007-06-03T03:20:00.000-07:00

Fs xlt bzk oazr qdfp, cfua xltopais z mzq lk qda ezbh.

Clue : substitution keyword ZEBRAS.

2007-05-26T00:29:00.000-07:00

Make 42 out of 2,3,4, and 9.
You may use each number once and only once using the arithmetic operations +,-,* and /.

Clocks

2007-05-19T22:00:00.000-07:00

1/ The hour and minute hands of a clock are superimposed at 12:00. When will they next be superimposed (I don't mean lined up as they are at 6:00)?
2/ Which has a better chance of giving the right time: a clock that has stopped or one that loses a minute every day?

An old one but a good one.

2007-05-12T06:12:00.001-07:00

Bob is 104. He is twice as old as Alice was when Bob was as old as Alice is now. How old is Alice?

Rope around the planet

2007-05-07T01:02:00.000-07:00

Imagine a rope that fits snugly all around a planet like a ring on a person's finger.
Now imagine the rope is made one metre longer and lifted off the surface until it is taut.
What will its height be above the surface of the planet?
(For the purposes of the puzzle, assume that the planet is a perfect sphere).

2007-04-29T07:49:00.000-07:00

Niels and Albert were excitedly describing the result of the International Puzzle Competition in Belgium. There were three contestants, Erwin, Werner, and Marie. Niels reported that Erwin won, while Werner came in second. Albert, on the other hand, reported that Marie won, while Erwin came in second.

In fact, neither Niels nor Albert had given a correct report of the results of the competition. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?

2007-04-22T02:29:00.001-07:00

You are lost in a forest. The forest is between two villages, A and B. People from village A always tell lies; people from village B always tell the truth. You want to go to village B.Then you see a man from either A or B. You can ask him only one question.Which question will you ask him to know for sure where village B is?

Roman numerals puzzle

2007-04-16T23:44:00.000-07:00

Roman numerals puzzle :-
You're given the symbols IX. Using any one symbol what would you have to add to it to equal 6?

Blind Beggar

2007-04-08T23:24:00.000-07:00

A blind beggar had a brother who died. What relation was the blind beggar to the brother who died? (Brother is not the answer).

Turkish Stampede

2007-03-31T06:16:00.001-07:00

During the Turkish stampede in Thrace, a small detachment found itself confronted by a wide and deep river. However, they discovered a boat in which two children were rowing about. It was so small that it would only carry the two children, or one grown person.
How did the officer get himself and his 357 soldiers across the river and leave the two children finally in joint possession of their boat? And how many times need the boat pass from shore to shore?

2007-03-14T11:54:00.000-07:00

Given two numbers, if we subtract half the smaller number from each number, the result with the larger number is three times as large as the result with the smaller number.
How many times is the larger number as large as the smaller number?

2007-03-06T13:34:00.000-08:00

There is an interesting five digit number A. With a 1 after it, it is three times as large as with a 1 before it. What is A?

2007-02-27T13:12:00.000-08:00

Five 3's can express 37 :-
37 = 33 + 3 + 3/3.
Find another way to do it.

Not about polar bears

2007-02-19T12:05:00.000-08:00

There's a well-known puzzle which is :- 'A bear hunter walks one mile south, one mile east, and one mile north, only to find himself back at his starting point. What colour is the bear he's hunting?'
The traditional answer is 'white' because with a starting point of the North Pole, someone walking one mile south, one mile east, and one mile north will find themselves back at the North Pole. Therefore the bear he's hunting must be a polar bear.
There are, however, a number of other points on the Earth's surface from where someone walking one mile south, one mile east, and one mile north will find themselves back at their starting point. Where are they?

2007-02-13T11:12:00.000-08:00

You have 50 pound coins on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < x < 50. You are asked to separate the coins into two piles in such a way that the number of heads up coins in both piles is the same at the end. You may flip any coin over as many times as you like. How will you do it?

2007-02-05T12:20:00.000-08:00

A number with two identical digits is multiplied by 99. What is the product if the third digit is 5?

Camel Race.

2007-01-29T10:15:00.000-08:00

A sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advise. After hearing the advice they jump on the camels and race as fast as they can to the city. What does the wise man say?

The Idler and the Devil

2007-01-23T12:48:00.000-08:00

An idler sighed, 'Everyone says, 'We don't need idlers. You are always in the way. Go to the devil!' But will the devil tell me to get rich?'
No sooner did the idler say this than the devil himself stood in front of him.
'Well', said the devil, 'the work I have for you is light, and you will get rich. Do you see the bridge? Just walk across and I will double the money you have now. In fact, each time you cross I will double your money.'
'You don't say!'
'But there is one small thing. Since I am so generous you must give me $24 after each crossing.'
The idler agreed. He crossed the bridge, stopped to count his money ... a miracle! It had doubled.
He threw $24 to the devil and crossed again. His money doubled, he paid another $24, crossed a third time. Again his money doubled. But now he had only $24, and he had to give it all to the devil. The devil laughed and vanished.
The moral: When anyone gives you advice, you should think before you act.
How much money did the idler start with?

Apples

2007-01-17T09:24:00.000-08:00

Five apples are in a basket. How do you divide the apples among five children so that each child gets an apple, yet one apple remains in the basket?

A Knight's Tour

2007-01-11T12:05:00.000-08:00

A knight is placed on the centre square of a 5 x 5 'chessboard' (or 5 x 5 area of an 8 x 8 chessboard, if you prefer).

Using only the legal moves for a knight in the game of chess, is it possible for the knight to visit every square in the 5 x 5 area?

2007-01-01T05:30:00.000-08:00

A contestant on a gameshow is given the choice of three doors.
Behind one door is a speedboat; behind the others, dusty bins.
The contests picks a door.
The host, who knows what's behind the doors, opens another door, which has a dusty bin.
He then says to the contestant, "Do you want to pick the third door or stick with your original choice?"
Is it to the contestant's advantage to switch doors?

Assume the following :-
- The contestant would rather win the speedboard than a dusty bin replica.
- The host is constrained to always open a door with a dusty bin.
- The host is constrained to always make the offer to switch.

Water Puzzle

2006-12-18T00:13:00.000-08:00

There are three glasses on the table - 3, 5, and 8 oz. The first two are empty, the last contains 8 oz of water. By pouring water from one glass to another make at least one of them contain exactly 4 oz of water.

Square Spiral

2006-12-11T00:03:00.000-08:00

Imagine a line running 100 paces east. Then from the end of that line, plant a line 100 paces north, then 100 west, 98 south, 98 east, 96 north, 96 west, and so on. This makes a square spiral path 2 paces wide. How long is the path?

Probability

2006-12-04T00:21:00.000-08:00

Ten letters are placed in ten pre-addressed envelopes at random. What is the probability that exactly nine letters were placed in the proper envelope?

2006-11-27T08:52:00.000-08:00

What's next?

1
11
21
1211
111221

Sets!

2005-03-20T05:33:00.000-08:00

Among 100 applicants for a scientific job, it was discovered that ten had no qualification in either physics or chemistry.

83 had a physics qualification. 75 had a chemistry qualification.

How many applicants had qualifications in both physics and chemistry? How many in physics but not chemistry? How many in chemistry but not physics?

Fox and Hen

2005-03-08T23:26:00.000-08:00

A hen and a fox have a combined age of 91.

The fox is now twice the age of the hen when the fox was as old as the hen is now.

How old are they?

(This puzzle found on the back of a beermat).

Bookworm Puzzle

2005-01-03T06:51:00.000-08:00

A bookworm eats from the first page of an encyclopaedia to the last page. The bookworm eats in a straight line.

The encyclopaedia consists of ten 1000-page volumes and is sitting on a bookshelf in the usual order. Not counting covers, title pages, etc., how many pages does the bookworm eat through?

(I found/stole this one from rec.puzzles some time ago - look it up if you like, but it's better to try and figure it out!)

Tony and George

2004-12-11T11:20:00.000-08:00

George Bush and Tony Blair were enjoying an expensive glass of apple juice in their local cafe when an odd mathematical situation occurred. The waiter brought them the bill for a whole number of US$consisting of four odd numbers.

"Hey", remarked the White House incumbent, "this bill is for exactly nine times too much".
"No worries", replied the denizen of Downing Street, "Just cross out the first digit and it's correct." And, being known as Teflon Tony, he was of course right. What did they pay?

Beer and Wine

2004-12-04T05:37:00.000-08:00

Of six barrels of capacity 15, 16, 18, 19, 20 and 31 litres respectively, five are filled with wine and only one with beer. A customer bought two barrels of wine, and then a second customer also bought wine, but of a quantity twice as much as the first.

Which is the beer barrel?

Roman Numerals Puzzle

2004-11-27T02:11:00.000-08:00

Reader, whether man or woman
Write my age in figures Roman
Three lettered units then you'll find
Each of the different in kind;
The first divided by the second
Will give the third, if rightly reckoned
Ten times the whole will let you see
My University degree

?

Word Puzzle

2004-11-13T03:26:00.000-08:00

Which well-known words or phrases are represented by the codes below?
1/ SIOUTDE
2/ BUR
3/ DISUMMERAN
4/ CCCCCCC
5/ $$$PINNER

Logic Puzzle

2004-11-06T05:14:00.000-08:00

Three men named Lewis, Miller, and Nelson work as accountant, cashier and clerk in the same department store.

If Nelson is the cashier, Miller is the clerk.
If Nelson is the clerk, Miller is the accountant.
If miller is not the cashier, Lewis is the clerk.
If Lewis is the accountant, Nelson is the clerk.

What is each man's job?

743403 is he dead

2004-10-31T17:52:00.000-08:00

Listen carefully and then tell us a secret about yourself. dbcghajghb

Mathematical Verse

2004-10-30T05:45:00.000-07:00

This is a mathematical poem from India. It's quite easy to solve once you get the hang of it :-

O beautiful maiden with beaming eyes, tell me,
Since you understand the method of inversion,
What number multiplied by 2,
Then increased by three quarters of the product,
Then divided by seven,
Then diminished by one third of the result,
Then multiplied by itself,
Then diminished by 52,
Whose square root is then extracted,
Before 8 is added and then divided by 10,
Gives the final result of 2?

Answers in the comments. :)

Another Pouring Puzzle

2004-10-23T04:46:00.000-07:00

Suppose that you have access to an 11-gallon container, a 6-gallon container, and a source of running water (such as a water tap). You do not have access to any measuring devices, but you are allowed to pour water down a drain.

How would you set about measuring out 8 gallons of water?

Answers in the comments please. Another puzzle in about a week.

Pouring Puzzle

2004-10-15T23:36:00.000-07:00

You have 3 containers, labelled A, B and C.
Container A has a capacity of 8 litres; container B has a capacity of 5 litres; container C has a capacity of 3 litres.
Currently, container A is full to the brim with water, whereas B and C are empty.
You are allowed to transfer water from any one container to the other, but are not allowed to use external water sources such as taps (so no pouring water down the drain and re-filling). You have no access to measuring equipment, and you are not allowed to 'guesstimate' water levels by eye (so, for instance, you cannot pour water from A to B and then do a visual check that they are approximately the same level, or 'half full').

What steps do you need to take to get to a state where 4 litres of water are in A, 4 litres of water are in B, and C is empty?

Two Travellers

2004-10-09T07:34:00.000-07:00

Two walkers spend from 3 pm until 9 pm walking along a level road, walking up a hill, and reversing their steps down the hill and back along the level road to return back home again. Their pace on the level is 4 mph, uphill 3mph, and downhill 6 mph.

How far did they walk?
To the nearest half hour, at what time did they reach the top of the hill?

Answers in the comments please.
The next puzzle will about a week from when this one was published!

Puzzle Competition

2004-10-02T01:31:00.000-07:00

Three puzzle competitors are blindfolded. A white piece of paper is glued to each competitor's forehead and they are told that not all of the pieces of paper are black. The blindfolds are removed and the competitors are told that the prize will go to the first to deduce whether the paper on his forehead is black or white.
The three competitors are silent for a short time, then all three announce white at the same time. Why?

Answers in the comments please. Note that there are two possible answers to this one - one relatively easy and intuitive, one harder and more 'logical'.

Counters

2004-09-25T07:25:00.000-07:00

A bag contains one counter, which has a 50/50 chance of being black or white. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?

Please comment on this post to propose an answer.
Answer in approximately one week.

NB :- I do enjoy puzzles, and I have written my own for a bit of fun on a MUD I used to frequent, but I'm far too busy/lazy to write my own for the purposes of this blog, which is intended as a bit of fun for regular readers of plep and anyone else who may happen by (though I may well recycle some of the puzzles I wrote all those years ago). I'm sure you could find the answer on the WWW with a bit of searching skill (this is an old puzzle - very old, in fact), but solving the puzzle by yourself is far more fun, believe me!