Web Puzzles

Island X Puzzle Solution

Assume that A is the Truther. If so, then B is the Liar as A's statement asserts. If so, B's second statement is false, so C is the Alternator. This implies that C's first statement is false as also his second statement that A is the Liar, so that C is the Liar which is a contradiction, so that A cannot be the Truther.

Assume that B is the Truther. If so, his first statement is a direct contradiction, implying amongst other things, that B cannot be the Truther.

Assume that C is the Truther. If so, then A is the Liar in conformity with his second statement, so the remaining member B must be the Alternator. This checks out since as a Alternator, B's first statement is true while in his second statement he falsely identified C as the Liar. Both of A's statement are then clearly false, so this establishes the veracity of both the statements of C.

Consequently, (A, B, C) = (Liar, Alternator, Truther)

A Farmer's Good Fortune Puzzle Solution

Here's one combination:

 94 sheep =  $470
  1 pig   =   $30
  5 cows  =  $500
-----------------
100 heads = $1000

Are there anymore?

A Special Old Guy Puzzle Solution

Firstly, we can say that the date of birth (DOB) for the special old guy (SOG) is:
Equation {a}:
DOB(SOG) = x^2 – x

Similarly, for the son of the special old guy (or SOSOG for short):

Equation {b}:
DOB(SOSOG) = y^3 – y

SOG's age when SOSOG was born was:
Equation {c}:
Age(SOG) = DOB(SOSOG) – DOB(SOG) = (y^3 – y) – (x^2 – x)

There are unlimited solutions to equation {c} so we need some assumptions and limits.

We know that SOG must have been between, say 10 years old and 100 years old when SOSOG was born:

Equation {d}:
10 < Age(SOG) < 100

We also know that both SOG and SOSOG were born some time since the year 500 AD:
Equation {e}:
500 < DOB(SOSOG) < 2004.

Based on equation {b} and {e} we can clearly see that there are only 5 solutions for y. They are y = 8, 9, 10, 11 or 12. Any other solutions for y are in breach of equation {e}.
For each of these possible solutions for y there is only a limited number of solutions for x that comply with {d}. They are:

 x     y
--------
21     8
22     8
26     9
27     9
31    10
36    11
41    12

Any other solutions for x and y are in breach of equation {d}.
SOG's age when his son was born can be calculated for each of these possible solutions by using equation {c} as follows:

 x      y     Age(SOG)
----------------------
21      8           84
22      8           42
26      9           70
27      9           18
31     10           60
36     11           60
41     12           76

So there are 7 different solutions, which is why Buzz said he couldn't solve for x and y.
Now comes the lateral part of the puzzle: Alvin informs Buzz that "...he was your age when his son was born". Of course, Buzz knows his own age. He should therefore be able to pick the correct solution from the list of 7 possible solutions shown above. However, he can't. That means that Buzz (and the special old guy) must be 60 because there are multiple solutions for an age of 60, whereas any other age would yield a unique solution. Any other age and Buzz would be able to solve.
A 60 year old father – quite a special old guy.

Switching Logic Puzzle Solution

Turn switch #1 ON. After about five minutes or so, turn switch #1 OFF and turn switch #2 ON.
Then go upstairs and check on the bulbs.

The one ON is obviously #2. The other ones are OFF, but one of them should be very hot by having been ON for five minutes. That's #1, and the remaining bulb is #3.

Boxes, Beads, and a Blindfold Puzzle Solution

The king puts 1 black bead in 3 of the 4 boxes and all the other beads (both black and white) in the fourth box.

In the kings' view, you will just randomly pick a box because you are so stupid. This gives you barely 1 chance out of 8 to pick a white bead (1/4 to pick that one box containing white beads multiplied with almost 1/2 to pick a white bead out that box).

Assuming each of the four boxes are identical, by picking up each box in turn, you will be able to tell by weight or the rattling noises which one of the boxes contains the mixed beads. Picking the box with the mixed beads will mean that you have a slightly better than 50% chance of living.

Thanks to "Ben Leil" and "Kobold" for posting solutions in the forum

Which Chest Is Which Puzzle Solution

Arthur does not need to open any chests.

Since all labels are on the wrong chests, the chest labelled GOLD OR SILVER COINS cannot contain either gold nor silver, so must contain bronze. Thus the chest labelled GOLD COINS must contain silver coins, and SILVER COINS must contain gold.

U2 Gig Puzzle Solution

The trick is to get the two slowest people to cross at the same time. One solution is...

• Bono and Edge cross the bridge for which they take 2 mins (Total time = 2)
• Then Bono comes back with the torch (Total Time = 2 + 1 = 3)
• Then Adam and Larry cross the bridge (Total time = 3 + 10 = 13)
• Then Edge comes back (Total = 13+2 = 15)
• Then both Bono and Edge cross the bridge (Time = 15+2=17)

Duck Hunt Puzzle Solution

Four ducks in a single row would do it.

The Devil's Muse Puzzle Solution

It's a palindrome.

The Diagram Puzzle Solution

Joe counted how many times each of the 7 LEDs lit up for all 10 digits...

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How Many Monks? Puzzle Solution

The way they work this out and the reason it happens on the same day is as follows. It is important to note that not only are the monks intelligent but they all know all their fellow monks are as well.
Start with one monk:

He knows he is the only one who can have the disease so he kills himself on
day 1.

Then two monks:
They know that either one of them has the disease or both do. If monk1
doesn't see the mark of the disease on monk2 then he will realise that he
must have it so will kill himself. If he sees the mark then he knows that
monk2 will following the same reasoning and kill himself. If the next day
the other monk is still alive then he realises that the other monk must have
seen the mark on him and so they both have the disease and he must kill
himself. Both follow the same reasoning and kill themselves on day 2.

Three monks:
If only one of the monks has the disease he will see no mark on the other
two and so diagnose himself. He will kill himself on day one. If two monks
have the disease then they will each see one monk with the mark and one
without. When they see each other again the next day they will deduce that
the monk they see with the mark would only not have killed himself if he
could see someone else with the mark. They know it is not the third monk so
it must be them. Both diseased monks follow the same reasoning and kill
themselves on day two. If all three monks have the disease then they are all
in the same position as the healthy monk in looking on in the previous
example. Each of them can see two diseased men. When they haven't both
killed themselves on day two there can be only one reason - the viewing monk
must have the mark as well. All taking the same reasoning they all kill
themselves on day three.

And so on...
N monks all with the disease will all kill themselves on day N.

The Geneaology Puzzle Solution

Page 1 in a book is the page just inside the front cover. Page 2 is the other side of the same sheet.

Pages 1201 and 1202 are opposite sides of the same sheet of paper, so finding something between these two is highly improbable.

How Old is the Vicar? Puzzle Solution

The vicar is 50.

The way to solve this puzzle, is to first of all write down all the possible permutations of three numbers whose product is 2450.

Starting Numbers	Product	Sum	Choirmaster
1, 1, 2450	2450	2452	1226
1, 2, 1225	2450	1228	614
1, 5, 490	2450	496	248
1, 7, 350	2450	358	179
1, 10, 245	2450	256	128
1, 14, 175	2450	190	95
1, 25, 98	2450	124	62
1, 35, 70	2450	106	53
1, 49, 50	2450	100	50
2, 5, 245	2450	252	126
2, 7, 175	2450	184	92
2, 25, 49	2450	76	38
2, 35, 35	2450	72	36
5, 5, 98	2450	108	54
5, 7, 70	2450	82	41
5, 10, 49	2450	64	32
5, 14, 35	2450	54	27
7, 7, 50	2450	64	32
7, 10, 35	2450	52	26
7, 14, 25	2450	46	23

Since the choirmaster, after being told that the product of the ages is 2450 and that the sum is twice his age, still can't work out the ages, we can deduce that there are two (or more) combinations with the same sum. Those combinations have been highlighted in the table above.

The vicar then claims to be older than all of them. The oldest of the three is 49 in the first remaining combination, and 50 in the other. The choirmaster knows the vicar's age, and after his claim, he deduces everyone's age. The only way he's able to do so is if the vicar is 50, leaving the combination 7, 7, 50 logically impossible (the vicar has to be older, that is at least 1 year older than the others), and therefore learning that the people's ages are 5, 10, and 49.

The Maze Puzzle Solution

If there are only T junctions, then all you have to do to get back is take all of the side passages that you come across, as they are the T junctions that were taken from your original perspective.

Effectively, every side passage you come across was a T junction that was taken earlier.

Of course, defining this the "ultimate" maze was a bit of an exaggeration on our part...

Four Hats Puzzle Solution

C saves the day.

D clearly has the most information at his hands, but seeing one white and one black hat doesn't give him any certainty about his own hat's colour. Would B and C both have been wearing the same colour, D would have been able to provide the answer.

But C is one clever guy and he knows that if D doesn't answer, it means that B is wearing a different colour than him. Because B is wearing white, C knows he's wearing black.

Note that A is redundant: the puzzle could have included only B, C, D. That way, the hats would have been three, with two hats of the same unspecified colour, and one other hat of the opposite colour.

Alan and Bert Puzzle Solution

Starting Numbers	Sum	Product	Product can also be made using
6, 5	11	30	10, 3
7, 4	11	28	14, 2
8, 3	11	24	6, 4 and 12, 2
9, 2	11	18	6, 3 and 9, 2

Bert knows that there are four possibilities for the starting numbers - so it is impossible to work out the starting numbers using the sum alone.

As mentioned in the question, he's quite clever - so he looks at the product that would appear if he used each of the four possible combinations. As shown in the table above, the product that appears can also be made from different numbers.

So, he announces that it is impossible for him or Alan to work out what the original numbers were. He seems to be on fairly safe ground.

Alan is a little bit more devious as well as being clever. Armed with this snippet of information he needs to look for a pair of numbers that give a non-unique sum and also give a non-unique product.
11 is the only non-unique sum which always gives a non-unique product. Alan is very clever and very smug.

Weighing an Elephant Puzzle Solution

Load the elephant onto a boat large enough to carry it. The boat will sink slightly, and you mark the level of the water on the side of the boat. Then you offload the elephant and fill the boat with bags until the boat sinks to the level marked. The bags can be individually weighed using beam scales and the weight of the elephant is the sum of the weight of the bags.

This puzzle is slightly cunning in that it the geographic location of the city is a small clue.

Carpet Layer Puzzle Solution

The only measurement that needs to be taken is the distance between opposite angles of the rectangular dance floor (figure on the left). That distance then will be squared (figure on the right) and doubled to get the sum of the areas of the 4 squares.

The Farmer's Problem Puzzle Solution

There are two solutions:

Solution A:
1) John takes the goat to the other side, and leaves it there.
2) He then takes the wolf to the other side.
3) He brings the goat back.
4) He takes the cabbages across, leaving them with the wolf.
5) John Comes back for the goat.

Solution B:
1) John takes the goat to the other side, and leaves it there.
2) He then takes the cabbages to the other side.
3) He brings the goat back.
4) He takes the wolf across, leaving it with the cabbages.
5) John Comes back for the goat.

Loadsa Coins! Puzzle Solution

You reach out and pick any 20 coins, and turn each of them over. The 20 coins is one group, and the remaining coins the other.

"Bugger," says Greed. "Why didn't I think of that?"

"It's so simple, yet so difficult to think of," you say. "Now can I have my eyesight back? Hello? Hello......!?"