# Web Puzzles

Showing posts with label puzzle game. Show all posts

## A Special Old Guy

Alvin and Buzz are nerds and like doing nerdy things. So Alvin called Buzz one day...

"Buzz, I've finished tracing my family tree back from the year 500 AD, and I found one quite special guy".

"Well, he was x years old in the year x^2 (x squared) and he had a son who was y years old in the year y^3 (y cubed)".

Buzz looked perplexed "Sorry Alvin, but I can't solve for x or y".

"Well, he was your age when his son was born." said Alvin.

"You're right" said Buzz "He was a special old guy! But I still can't solve for x or y".

How old was the old guy when his son was born?

Notes:
Assume that the nerds have the conversation this year, ie 2004 AD.

### 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.

## Which Chest Is Which

One day Arthur came to Merlin and asked him, "Show me how to be a wise and good king." Merlin replied, "If you can pass a series of mental tests, I will teach you".

Merlin then showed Arthur three chests, one was labelled GOLD COINS, the second was labelled SILVER COINS, and the last, GOLD OR SILVER COINS. He stated that all the three labels were all on the wrong chests. Given that one chest contained gold, one silver, and one bronze.

How many chests must Arthur open to deduce which label goes on which chest?

### 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.

## Duck Hunt

Tim and Tom were playing their Dad's old favourite game machine - a classic Nintendo Entertainment System (NES). The game was, surprisingly, Duck Hunt. Tom was at the controls, shooting innocent ducks with the lightgun.

Tim pokes Tom, and whines, "let me play." Tom looks back, and Mum is looking at them, so Tom begins to feel generous.

"Tell ya what, Tim. If you can answer a riddle about ducks, you can play. Otherwise, I get a half an hour more."

Tim, who occasionally can be a dunce, happily says "OK!".

Tom asks his question, "How many ducks do you have if you have two ducks in front of two ducks, two ducks behind two ducks, and two ducks between two ducks?"

Tim is stumped. "15?"

"Nope," says Tom.

"12?"

"Nope."

Exasperated, Tim says, "Ok, what is the answer?"

When Tom tells him, Mom goes off smiling, Tim stomps off, and Tom gets the high score on the game.

What it the least number of ducks to meet the conditions?

### Duck Hunt Puzzle Solution

Four ducks in a single row would do it.

## The Devil's Muse

It's everybody's fate, but unfortunately for you today it's yours. You die and wander through a long tunnel towards a light. But, wait a second, that's not white light? It's crimson red!

Indeed, going through the gate at the end you face an enormous deity, cloaked in flames, holding a gigantic trident in one hand. On this trident you can make out two bodies speared to it... beads of sweat start to form on your forehead, and they're not from the heat that's omnipresent in this room.
"Hahaha", the Devil laughs, "don't be afraid. You won't necessarily end up like them... they're just the souls of Mickey and Tung. They sold them to me in exchange for the ability to create awesome websites, or something like that, never kept contact with them though... Now, the fact you're here is that this millennium it's my turn to decide who goes to Heaven and who goes to Hell. St. Peter really needed that 1000 year vacation, so I'm on duty now. Since I'm the boss, I get to decide who goes where. And, to be completely honest, this 'Good/Bad'behaviour thingy... it's a bit outdated, isn't it ?

And so the Devil starts to recite :

Evil am I.
Evil,
as so to die not sane.

Menace I lay.
A stab mocks.
I revolt.
No din is still.

I kidnap and I kill.
It's sin I don't love.
Risk combat.
Say a lie.

Cane men.
A stone I do toss!
Alive,
I'm alive.

"Now", the Devil says. "If you can point out the single most peculiar thing about this poem to me, I'll let you go and you can take that elevator over there.... what ? ... yeah yeah, the one with hostesses dressed like poultry at its doors... now start thinking, 'cause I ain't got all day!".

Right at that moment you notice that there's still one spike unoccupied on Satan's trident...

What is so special about the Devil's poem?

### The Devil's Muse Puzzle Solution

It's a palindrome.

## How Old is the Vicar?

There once was a choirmaster.
One day three people came in and asked to join the choir.
The choirmaster, who believes that there should be age for his choir's members, asks their ages.

To that question, one of them replied: "We can't tell you our ages, but we can tell you the following: the product of our ages is 2450, and the sum of our ages is twice your age."

The choirmaster is puzzled: "That's not enough information!"

Just then, the vicar walked in and said: "But I'm older than all of them"

The choirmaster, who knew the vicar's age, then exlaimed: "Ah! Now I know."

How old is the vicar?

### 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.

## Carpet Layer

Walter Wall is a carpet layer. He and his two apprentices are asked by a nightclub owner to give a quote on laying carpet.

The owner indicates an oblong dance floor (figure on the right) and tells them that he wants a square of carpet adjacent each of the sides and running its entire length, making four squares in all (figure below left).

Walter asks both apprentices how many measurements must be made to calculate the total area of carpet needed in order to give a quote.

Sam, the slower of the two, replies that eight measurements are needed: two sides of each square.

Walter reprimands him, reminding him that these are squares and therefore have all sides the same length, and that they are in identical pairs, "So we only need to take two measurements - one side of one of the large squares and one side of one of the smaller squares".

Brian, the bright apprentice, points out that they can give the quote after taking only one measurement.

How can the total area (that is, the sum of the areas of the four red squares) be calculated by taking just one measurement?

### 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

Farmer John had a problem. There were a group of brigands that had taken all he had... except for three things: his prized wolf, his goat, and a box of cabbages. They were coming after him, to get the rest. These brigands did not like water, so John went to the Blue River, a deep, fast river that no one could swim, and it had no bridges. He always kept a boat there, because he liked to fish, but it was small. So small, in fact, that he and only one of his precious things could be in the boat at the same time.

It sounds simple, right? Ferry one item across at a time, and come back for the others? Well, if John leaves the goat with the cabbages alone on one side of the river the goat will eat the cabbages. If he leaves the wolf and the goat on one side the wolf will eat the goat. If john is there, only he can seperate the wolf from the goat and the goat from the cabbage.

How can farmer John keep his possessions safe from the brigands, without losing a single one?

### 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.

## TV Show

The host of the show pointed at three doors. He claimed that, behind one of the doors, a brand new sportscar was awaiting a lucky winner. The other two doors, he warned, did not lead to any prize.

The contestant picked the first door as his guess. At that point, the host walked to the third door and opened it. The door led to no prize, which is something the host knew perfectly well. He then gave the chance to the contestant to switch and pick the second door, if he so wished, or to stick to his first choice and stay with the first door.

Did the contestant have a greater chance of winning the car, by sticking with the 1st door, or by switching to the 2nd door? Or were the chances equal?

Notes:
The contestant knew three things: first, that the host doesn't want him to win; second, that the host was going to open one of the doors; and third, that the host would never open the door picked by the contestant himself... regardless of where the prize really is.

### TV Show Puzzle Solution

This puzzle isn't particularly new, but it became very well known in 1990, thanks to the person that allegedly had "the highest IQ ever recorded" -- 228, according to The Guinness Book of WorldRecords. Miss Marilyn vos Savant (yes, it was a female) wrote a solution to this puzzle on her weekly column, published in a popular magazine. This solution led to waves of mathematicians, statisticians, and professors to very heated discussions about the validity of it.

The contestant, according to vos Savant, had a greater chance of winning the car by switching his pick to the 2nd door.

She claimed that by sticking to the first choice, the chances of winning were 1 out of 3, while the chances doubled to 2 out of 3 by switching choices. To convince her readers, she invited her readers to imagine 1 million doors instead of just 3. "You pick door number 1," she wrote, "and the host, who knows what's behind every door, and doesn't want you to win, opens all of the other doors, bar number 777,777. You wouldn't think twice about switching doors, right?"

Most of her readership didn't find it as obvious as she thought it was... She started receiving a lot of mail, much of it from mathematicians, who didn't agree at all. They argued that the chances were absolutely equal, whether or not the contestant switched choice.

The week after, she attempted to convince her readers of her reasoning, by creating a table where all 6 possible outcomes were considered:

 Door 1 Door 2 Door 3 Outcome (sticking to door 1) Car Nothing Nothing Victory Nothing Car Nothing Loss Nothing Nothing Car Loss Door 1 Door 2 Door 3 Outcome (switching to other door) Car Nothing Nothing Loss Nothing Car Nothing Victory Nothing Nothing Car Victory

The table, she explained, shows that "by switching choices you win 2 out of 3 times; on the other hand, by sticking to the first choice, you win only once out of of 3 times".

However, this wasn't enough to silence her critics. Actually, it was getting worse.

"When reality seems to cause such a conflict with good sense," wrote vos Savant, "people are left shaken." This time, she tried a different route. Let's imagine that, after the host shows that there's nothing behind one of the doors, the set becomes the landing pad for a UFO. Out of it comes a little green lady. Without her knowing which door was picked first by the contestant, she is asked to pick one of the remaining closed doors. The chances for her to find the car are 50%. "That's because she doesn't have the advantage enjoyed by the contestant, ie the host's help. If the prize is behind door 2, he will open door 3; if it is behind door 3, he will open door 2. Therefore, if you switch choice, you will win if the prize is behind door 2 or 3. YOU WIN IN EITHER CASES! If you DON'T switch, you'll win only if the car is behind door 1".

Apparently, she was absolutely right, because the mathematicians reluctantly admitted their mistake.