Picture This

[billfaceuk]

Theres a frog on one side of a road. The road is 10 metres wide. The forg's object is to get to the other side of the road. His first jump is 5m his second 2.5m and for every other jump he does the length halfs.

Eg:

1st-5m
2nd-2.5m
3rd-1.25m
etc

How many jumps will it take the frog to get to the other side? I don't actually know the answer and I ain't very good at maths in the vb environment but I would still be interested in the equation to find this answer out.

Thanx!

[Yonatan]

This looks like something based on some extremely old math riddle.
The answer is that the frog will never reach it. (Or, it will reach it after infinite jumps, if possible)
I can prove it mathematically:
Lets say A(n) is the distance after n jumps.
Thus, A(n) is an infinite geometric sequence (I THINK that's what it's called in English, I studied maths in Hebrew so I don't know the English terms).

Given:
A(1) = 5
Q = 0.5

Now, there is a formula for the sum of an infinite geometric sequence where the 'Q' (quotient) is between 0 and 1:

S = A(1) / (1 - Q)

In this specific problem:

S = 5 / (1 - 0.5) = 5 / 0.5 = 10

So, after infinite jumps, the frog will finally pass the 10 meters.

If you don't know about sequences, here's the (sort of) basic idea:
First the frog has a specific distance to pass.
Then it will pass half of that, and will have a new distance to pass.
But it can only pass half of that, so it will then have an entirely new distance to pass.
And so on and so forth.
So, no matter how many times it jumps half the distance, it will always have a whole new distance to pass, and this distance cannot be passed by jumping half of it.
The answer is infinity, and you should remember that infinity is not a number, it is a concept - and in this case it means the frog will never get to the other side.


Besides, why did the frog cross the road?

[billfaceuk]

but as long as the frog is always moving forward and he never hits negative numbers (which isn't possible) he will be getting closer and by the time he did make it about half way, a car would have run him over

[Guv]

I am reminded of a story about a mathematician and an engineer whou died and went to hell.

They were placed in a large room with beautiful, naked, willing women at the other end of the room.

They were told that when they tried to approach one of the women, they would only be able to cover half the distance to the objective with each attempt.

The mathematician sat down and cried because he knew that the rules would prevent him from getting to one of the women.

The engineer smiled and said

I can get close enough for all practical purposes

[parksie]

Good point
Now on to the practical purposes.......

[Asaf_99]

Probably, or he'll just get bored and go to sleep:P
Anyway, I had this stupid old question on 2nd(?) grade and the teacher compared it to a kid trying to reach another kid (Don't ask me!).
She's dumb.

Yonotan (Yonatan), he'll never reach it even after(?) infinite jumps, because he only goes half of what's left.
Anyway, the from would've died if he'd do infinite jumps or he'll just break(?) his leg(?).

[billfaceuk]

Solve this one:

Three men go to a hotel. They ask the clerk, "How much is a room?" and
the clerk tells them it is $30. They each pay the clerk $10 and go to the room. The clerk knew that the room rate was really only $25 and started to feel guilty about overcharging the men so he gave the bellboy a $5 bill and told him to return the money to the men.
The bellboy knew that $5 didn't divide evenly among the three men, so he
kept the $5 bill and returned one dollar to each of the men, keeping the extra $2 for himself.

So each of the three men paid $9 for the room ($27 total) and the bellboy kept $2. Where is the other dollar?

[Yonatan]

Correction:

Lets say A(n) is the distance after n jumps.

I meant to say: Lets say A(n) is the distance that the frog jumps during the n-th jump.

by the time he did make it about half way

That's after the first jump

Anyways, I wrote a quick and silly program based on the vague mathematical ramblings that I rambled about:

Option Explicit

Sub Main()
    Dim Current As Double, Total As Double
    Dim I As Long
    
    Current = 5
    
    Do
        Total = Total + Current
        Current = Current * 0.5
        I = I + 1
    Loop Until Total = 10
    
    Debug.Print I
End Sub

I know that Total would reach 10, because the FPU (Floating Point Unit) doesn't really calculate up to 17,000 digits after the decimal, and it would be too inaccurate at some point - I just wanted to know when.

The output showed 53. Less than I expected, but I'll get over it.

Nice stories

Asaf: Thou shalt think not of infinity as a number in actuality, but behold it as a concept.
After infinite (warning! not a number!) jumps, the frog will reach the destination. He won't actually reach it, of course, but he'll get closer and closer, and in infinity (warning! not a number!) he'll get there.

I know you won't understand this so I'm saying it on purpose : If you draw the graph of S(n) - the formula for the distance after n jumps which I didn't calculate yet and probably won't - you will find a horizontal asymptote: y = 10
This is because:

lim S(n) = 10
n->infinity

The definition of asymptote is exactly this - it meets the function at infinity (but doesn't actually meet it using real numbers).

Besides, when you get to differential maths (around 11th grade or so) it'll all make sense to you.

[Yonatan]

Originally posted by billfaceuk
Solve this one:

Three men go to a hotel. They ask the clerk, "How much is a room?" and
the clerk tells them it is $30. They each pay the clerk $10 and go to the room. The clerk knew that the room rate was really only $25 and started to feel guilty about overcharging the men so he gave the bellboy a $5 bill and told him to return the money to the men.
The bellboy knew that $5 didn't divide evenly among the three men, so he
kept the $5 bill and returned one dollar to each of the men, keeping the extra $2 for himself.

So each of the three men paid $9 for the room ($27 total) and the bellboy kept $2. Where is the other dollar?

Someone on ICQ told me this once:

the answer is that there is no answer.
while in a parallel univerise the dollar was lost. only 29 dollars made it out alive.

such a tragic day in history.

[billfaceuk]

I wrote a program to work out the jumps does this work???

Do Until i=10
     i= i / 2
Loop

It did crash my computer though

So does this code work?

[billfaceuk]

Now the dollar is not losed see this example.

When you count the fingers on your left hand 1-5 like below you count your five fingers!


When you count the fingers on your right hand backwards your fifth finger is number 6.


6+5 =11 but we have 10 fingers it works on this principle. Kind of!

[Lord Orwell]

Originally posted by billfaceuk
Solve this one:

Three men go to a hotel. They ask the clerk, "How much is a room?" and
the clerk tells them it is $30. They each pay the clerk $10 and go to the room. The clerk knew that the room rate was really only $25 and started to feel guilty about overcharging the men so he gave the bellboy a $5 bill and told him to return the money to the men.
The bellboy knew that $5 didn't divide evenly among the three men, so he
kept the $5 bill and returned one dollar to each of the men, keeping the extra $2 for himself.

So each of the three men paid $9 for the room ($27 total) and the bellboy kept $2. Where is the other dollar?

What extra dollar? You SUBTRACT the two dollars from what they paid, not add it.
they paid $25 for the room and 2 to the bellboy.
9 * 3 = 27

[Lord Orwell]

Originally posted by billfaceuk
Now the dollar is not losed see this example.

When you count the fingers on your left hand 1-5 like below you count your five fingers!


When you count the fingers on your right hand backwards your fifth finger is number 6.


6+5 =11 but we have 10 fingers it works on this principle. Kind of!

What if i counted backwards on both hands?
109876
54321
6 + 1 = 7!
i have 7 fingers

[billfaceuk]

7????? FREAK

You could make millions, well until someone counted your fingers the right way round!

[Starman]

Perhaps the women, being willing and eager, approached the two gentlemen?