Math Puzzles!

I always liked this one:

[i]Three guests check into a hotel. The clerk says the bill is $30 so each pays $10. Later the clerk realizes the bill should only be $25. To rectify he gives the bellhop five dollars to return to the guests. On the way back to the room the bellhop realizes that he cannot divide the money evenly. As they didn?t know the total of the revised bill, he decides to give each guest a dollar and keep two for himself.

Now that the guests have been given a dollar back, each has paid $9. 3 x 9 = 27 and the bellhop has $2. 2 + 27 = 29. If the guests originally handed over $30, what happened to the remaining dollar?[/i]

If the cashier has 25 and the bellhop kept 2 and gave 1 to each guest isn’t that

25 + 2 + 1 + 1+ 1?

[quote]pookie wrote:
I always liked this one:

[i]Three guests check into a hotel. The clerk says the bill is $30 so each pays $10. Later the clerk realizes the bill should only be $25. To rectify he gives the bellhop five dollars to return to the guests. On the way back to the room the bellhop realizes that he cannot divide the money evenly. As they didn?t know the total of the revised bill, he decides to give each guest a dollar and keep two for himself.

Now that the guests have been given a dollar back, each has paid $9. 3 x 9 = 27 and the bellhop has $2. 2 + 27 = 29. If the guests originally handed over $30, what happened to the remaining dollar?[/i]

[/quote]

There is no missing dollar. The calculation of 3x9+2=29 fucked up because 27 = 25 + 2. So if you add 2 again you’re counting it twice and not counting the $3 returned to the guests at all.

the logic of the question is wrong.
as stated, if the guests paid 9 dollars each, they spent a total of 27 dollars.
adding the 2 dollars that the bellhop took to that amount is wrong because that amount is considered as part of the spent total already.

so to break it down for you:
rectified bill = $25
bell hop amount = $2
therefore, total money spent by guests = 25+2 =$27
amount given back to guests = $3

so in other words, there is no missing dollar.

[quote]pookie wrote:
I always liked this one:

[i]Three guests check into a hotel. The clerk says the bill is $30 so each pays $10. Later the clerk realizes the bill should only be $25. To rectify he gives the bellhop five dollars to return to the guests. On the way back to the room the bellhop realizes that he cannot divide the money evenly. As they didn?t know the total of the revised bill, he decides to give each guest a dollar and keep two for himself.

Now that the guests have been given a dollar back, each has paid $9. 3 x 9 = 27 and the bellhop has $2. 2 + 27 = 29. If the guests originally handed over $30, what happened to the remaining dollar?[/i]

[/quote]

Ha, the first time I heard that it had me stumped for ages.

Theorem: $1 = 1 cent

Proof:

$1 = 100c = (10c)^2 = ($0.10)^2 = $0.01 = 1c

I have a better proof that women are evil:

Women = Money x Time
Time = Money
Women = Money x Money = Money ^ 2

Money = (Evil) ^ (1/2) …"Money is the root of all evil)

Women = [Evil ^ (1/2) ] ^ 2

Women = Evil.

QED

[quote]pookie wrote:
Theorem: $1 = 1 cent

Proof:

$1 = 100c = (10c)^2 = ($0.10)^2 = $0.01 = 1c

[/quote]

You can’t include the unit inside the ()^2 function. There is no such thing as cents squared or dollars squared. The proof is flawed.

Man fuck math.

[quote]masonator wrote:
Man fuck math.[/quote]

That would be a mathemadickal puzzle.

[quote]pookie wrote:
masonator wrote:
Man fuck math.

That would be a mathemadickal puzzle.
[/quote]

Not so much.

[quote]masonator wrote:
pookie wrote:
masonator wrote:
Man fuck math.

That would be a mathemadickal puzzle.

Not so much.

[/quote]

A man-in-mathical one then?

I’ve got one for ya

A jar with germs

In a jar with 1 germ, the germ splits into two, two split into four germs , etc.
It takes ONE germ 1 hour to split so many time so that the jar is full.
How long does it take for TWO germs to fill the jar???

Age of the mother

On a sunny day a boy asks his father how old his mother is.
His father replies:" When I first met your mother I was TWICE the age of your mother.
But the next year I was only 1.5 times as old. How about that boy?"

The father is 44

How old is his mother?

(HINT: his parents were young when they met)

[quote]Erasmus wrote:
Age of the mother

On a sunny day a boy asks his father how old his mother is.
His father replies:" When I first met your mother I was TWICE the age of your mother.
But the next year I was only 1.5 times as old. How about that boy?"

The father is 44

How old is his mother?

(HINT: his parents were young when they met)

[/quote]

Is the answer to your other one: 2 germs cannot fill the jar, they would have to split into more?

[quote]Lancey wrote:
Erasmus wrote:
Is the answer to your other one: 2 germs cannot fill the jar, they would have to split into more?[/quote]

Surely the two germs would fill the jear in a little under 1 hour. There ARE two germs in the jar after the first divides for the first time.

OR two germs will never fill the jar, 'cos there’s only two of them (unless its a very small jar!)

[quote]Erasmus wrote:
I’ve got one for ya

A jar with germs

In a jar with 1 germ, the germ splits into two, two split into four germs , etc.
It takes ONE germ 1 hour to split so many time so that the jar is full.
How long does it take for TWO germs to fill the jar???[/quote]

1 hour minus the time for 1 split.

[quote]Boffin wrote:
Surely the two germs would fill the jear in a little under 1 hour. There ARE two germs in the jar after the first divides for the first time.
[/quote]

I kept re-reading the question trying to figure out what was so tricky about it. You are right, just a hair under an hour. I’m guessing people probably blurt out 1/2 an hour when they hear this.

[quote]Boffin wrote:
Lancey wrote:
Erasmus wrote:
Is the answer to your other one: 2 germs cannot fill the jar, they would have to split into more?

Surely the two germs would fill the jear in a little under 1 hour. There ARE two germs in the jar after the first divides for the first time.

OR two germs will never fill the jar, 'cos there’s only two of them (unless its a very small jar!) [/quote]

The reason I asked if that was the answer is because there’s no way to work out how long it takes without either knowing the amount of time it takes for each split or how many germs are needed to fill the jar

[quote]pookie wrote:
Erasmus wrote:
I’ve got one for ya

A jar with germs

In a jar with 1 germ, the germ splits into two, two split into four germs , etc.
It takes ONE germ 1 hour to split so many time so that the jar is full.
How long does it take for TWO germs to fill the jar???

1 hour minus the time for 1 split.
[/quote]

pookie got it.

One germ:

2^(60 minutes/time for one split = t) = # of germs to fill jar

Two germs:

2^(x/t) + 2^(x/t) = # of germs to fill jar

So:
2*2^(x/t) = 2^(60/t)

Take ln of both sides:

ln(2) + (x/t)ln(2) = (60/t)ln(2)

Divide both sides by ln(2):

1 + (x/t) = 60/t

Multiply both sides by t:

t + x = 60

x = 60 - t