[Guest]

A man has 10.3 cm of gold. He went to an Hostel to rent a room.

The owner of the hostel asked 1cm of gold for each night.

Then the man found in his room a machine that can cut the gold but at each cut he will loose 0.1 cm of gold.

So he did his calculation and he decided to stay 10 nights.

Can anyone tell me how can he stay 10 nights, while he had just 10.3 cm of gold and he has to pay one cm each night...

[Guest]

A man has 10.3 cm of gold. He went to an Hostel to rent a room.

The owner of the hostel asked 1cm of gold for each night.

Then the man found in his room a machine that can cut the gold but at each cut he will loose 0.1 cm of gold.

So he did his calculation and he decided to stay 10 nights.

Can anyone tell me how can he stay 10 nights, while he had just 10.3 cm of gold and he has to pay one cm each night...

paid for all 10 nights up front and kept .2 cm for himself.

[Guest]

I would guess he made one cut and paid all at once.

[Guest]

If we assume the owner is the kind of person who is willing to give change, does not have any change on hand, and is also willing to hold any of our friend's gold pieces as potential change for the duration of his stay. The man can cut his 10.3 cm chain into four pieces, 1cm, 2cm, 3cm, and 4 cm.

X.XX.XXX.XXXX

X XX XXX XXXX

Give 1 cm piece on the first night.

Give the 2 cm piece on the second night receiving his 1 cm back as change, repeating the process with the 3cm piece on the third night, etc. It's easier graphically.

1) X

2) XX

3) XXX

4) XXXX

5) XXXX X

6) XXXX XX

7) XXXX XXX

8) XXXX XXX X

9) XXXX XXX XX

10) XXXX XXX XX X

[Guest]

since the problem doesn't say what the other dimensions of the gold are, he could cut it into thin slices longitudinally, giving him multiple 10.3cm pieces for him to cut from.

But Cracked Corn's solution is probably what mojail was looking for.

Edited May 30, 2008 by MAD

[Guest]

he paid all at once,, and guess what he saved .2cm for him too

[Guest]

Cracked has it.

Pieces: 1,2,3,4

[font="Courier New"]
Day Man's Pieces Cashier's Pieces
1 432 1
2 431 2
3 43 21
4 42 31
5 41 23
6 4 123
7 3 124
8 2 134
9 1 234
10 0 1234[/font]

[Guest]

Cracked Corn got it right! Good Job

[Guest]

The man could fold the chain and cut multiple lenghts at the same time. He would have to double fold it but it could be done.

[Guest]

The man only has to make one cut at 10 cm., he will then have .2 cm. left because he lost .1 cm. when he cut the 10.3 cm. of gold that he had to start with.

[EventHorizon]

Of course....he could stay 15 nights with 15.3 cm of gold...

Yay for binary!

This reminds me of another puzzle....basically the same kinda thing, though I cannot remember the situation/wording exactly...so I'll copy yours somewhat.

You have a gold chain with 7 links. You don't have enough rent, but your landlord agrees to allow you to give him a gold link every day until you have the rent to get them back (he must be holding 2 links on day 2, 5 on day 5 etc). You don't want to make too many cuts, since you will be getting them back. How many cuts do you need to make if you are going get the money for rent in a week?

one!

But I won't say how....though it isn't rocket science

Follow-up questions:

1. If you have a chain of length 23 and will only make 2 cuts, how long could you delay rent?

2. If you have a chain of length 365 and want to delay rent a whole year....how many cuts are needed?

3. If you have a chain of length 4000 and want to delay rent for a decade....how many cuts are needed?

4. If you have a chain of length F(x) and want to delay rent for F(x) days.....only x cuts are needed, but x+1 cuts are needed if you had one link more and one day longer to delay. What is F(x)?

Spoiler for Are you sure you don't want to give it a try first?:

Spoiler for I'll only let you look if you really want to...:

Spoiler for Fine....here's the answer:

Spoiler for Hah! fooled you! Ok....here's the answers to the follow up questions:

Spoiler for 1:

23 days

Spoiler for 2:

5 cuts

Spoiler for 3:

8 cuts

Spoiler for 4:

x + (x+1)(2^(x+1)-1)

Do you see why?

Edited May 30, 2008 by EventHorizon