Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

Those are the 100 digit problems posed a few years ago.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Can you solve them all?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

You are joking of course?!???!!!!!!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Here are some more: http://www.siam.org/journals/problems/d … 04-003.pdf

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

Folkmar, unless I am mistaken was on one of the teams that got all ten right.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Steven created a problem inspired by one of those. It is not very hard, though.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

You solved it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Yes.

The person below did not expect that

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

I was expecting that answer.

Dost thou consider thyself wise in the ways of programming? Art ye ready for a challenge that hath stumped the mightiest?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Count Dooku wrote:

Good. Double the pride, double the fall.

No, I do not consider myself wise, because of the above principle. But I will look at your problem and try it.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

If thou art diligent and wise, O stranger, compute the number of cattle of the

Sun, who once upon a time grazed on the fields of the Thrinacian isle of Sicily,

divided into four herds of different colours, one milk white, another a glossy black,

a third yellow and the last dappled. In each herd were bulls, mighty in number

according to these proportions: Understand, stranger, that the white bulls were

equal to a half and a third of the black together with the whole of the yellow,

while the black were equal to the fourth part of the dappled and a fifth, together

with, once more, the whole of the yellow. Observe further that the remaining

bulls, the dappled, were equal to a sixth part of the white and a seventh, together

with all of the yellow

That problem was supposedly posed by a god, mine is somewhat easier.

There are 3 kegs of water. The first keg has 1 liter, the second keg has 2 liters and the third keg has 3 liters of water in it. Each day our traveller picks one keg at random with each keg having the same chance of being picked and takes and drinks one liter of water from it. When he empties a keg he throws it away. When he is left with one keg he records the amount of water in it. What is the expected amount of water remaining in that last keg?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

The answer is (125/72) according to RIES and I have verified that in two ways.

Using a simulation:

```
from random import choice
def simulate(kegs):
while len(kegs) > 1:
n = choice(range(len(kegs)))
kegs[n] -= 1;
if kegs[n] == 0:
del kegs[n]
return kegs[0]
ans = sum((simulate([1,2,3]) for i in range(1000000)))/1000000
```

and actually evaluating the probability tree:

```
import Data.List
type Keg = Float -- Capacity Water
type State = [Keg]
rots :: [a] -> [[a]]
rots xs = init (zipWith (++) (tails xs) (inits xs))
calculate :: State -> Float
calculate kegs = go 0.0 1.0 kegs
where
go :: Float -> Float -> State -> Float
go e p [w] = e + p*w
go e p kegs = foldr (\st e' -> go e' p' st) e newStates
where
newStates = [ f s | s <- (rots kegs) ]
f (1.0:ks) = ks
f (w:ks) = (w-1):ks
p' = p/(fromIntegral $ length newStates)
ans = calculate [1,2,3]
```

*Last edited by Agnishom (2016-12-27 01:07:50)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

You do not need RIES to rationalize a fp but very good, you solved the problem.

How high can your tree go? Can you do 2 to 10 kegs? A ten keg problem would be 1,2,3,4,5,6,7,8,9,10 liters per bottle.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

What is an fp?

I can only do upto 4 with the tree program. It grows rapidly

*Last edited by Agnishom (2016-12-27 13:08:34)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

Stands for floating point.

What was your answer for 4 then?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

1.9035132137345392

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

Your tree could not get an exact answer?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Post #17 is what I have.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

Okay, I have the exact answer already.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

How do you get it?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

By copy and paste.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

What is that again?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,190

I copied and pasted.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

In other words, you have more digits than I do.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline