Thread: Gold Chain Problem...

hi...............................>>>><>
what i think you have to cut 1 link at the last of every single link so that a son can give rent for 151 week if i am right you can tell me otherwise correct me

no rohit...that is not a correct answer.

Clue: The total number of cut is only 4. Try to find which place we are going to cut.

Hi Friends,

Here is my answer for this question...The mininum number of cuts needed to made is 4 for a chain with 151 links.

If the links are numbered serially from 1 to 151, then the cuts would be made n the following links. 6, 17, 38, 79.

So Now you have 4 one-link pieces, one 5-link piece, one 10-link piece, one 20-link piece, one 40-link piece and one 72-link piece.

To gain a better understanding, consider the scenerio in the first few weeks as illustrated in the table blow.

weeks - Gold links given

1 -------- 1
2 --------- 1+1
3 --------- 1+1+1
4 --------- 1+1+1+1
5 --------- 5 (get back the 4 one links)
6 --------- 5+1
7 --------- 5+1+1
8 --------- 5+1+1+1
9 --------- 5+1+1+1+1
10 -------- 10 (get back the one 5-link piece and 4 one link pieces)
11 -------- 10+1
12 -------- 10+1+1
.
.
.

Using the above format we can give a link for all the 151 weeks.


-------------------------
suresh

I have no clue abt ur solution.. i m nt able to understand.

what can i do? i can't able to explain simply other than this.

-------------------
suresh

Just an extension to this problem...

what would be the minimum number of links he would need to cut?
i. if the gold chain that consisted of 383 links
ii. if the gold chain that consisted of 159 links
iii. if the gold chain that consisted of 63 links
iv. if the gold chain that consisted of 23 links

are you able to generalize the solution

If you see my solution i am using 4 cut for 151 links. Also finally i got (5,10,20,40,76) set of links.

So using 4 cut you can satisfy maximum of 155 links.
(5,10,20,40,80)
The series is going (x,2x,4x,..)

So if we using 5 cut you can satisfy maximum of 378 links.
(6,12,24,48,96,192)

If we using 6 cut you can satisfy the maximum of 889 links.
(7,14,28,56,112,224,448)

I don't have any generalized solution for this. Because i see this puzzle in somewhere place.

--------------------
suresh

The generalized formula is,
By using 'n' cut you can get up to maximum of (n+1) 2^(n+1) -1 links.

And

So using 4 cut you can satisfy maximum of 155 links.
(5,10,20,40,80) is wrong...you can get up to 159 links ( 5+10+20+40+80 + 4 links ) by making 4 cuts.

Hi Suresh,

In your question, it says "He was required to pay every week one link of the gold chain as rent for the place..." Considering this fact, I think the minimum number of cuts will be 151.

Explanation: When he has to pay for the first week, he will cut the chain twice - he has to cut the chain frist, then remove one link (one more cut) and pay the land lady. At the end of 150 weeks, 151 cuts would have gone, but for final link he needn't cut the chain anymore.

The 2nd para stating, "The landlady told him that she wanted one link of the gold chain at the end of one week, two gold links at the end of two weeks, three gold links at the end of three weeks and so on"; I suppose it's given to confuse people, bcoz anyway as 1 week adds on, one more link comes to her every week, and she will have the number of links stated.

Am I right ???

Cheers,
Srilatha.K

I think minimum cut should be 4

because if u cut into following pattern
1 6 17 38 79 151
---------------------------------------------------------
^ ^ ^ ^
^ means cut
now no. of single links are (1+1+1+1) in 4 places cut

and other 5 pieces are 1. 5 links
2. 10 links
3. 20 links
4. 40 links
5. 72 links


for week
1=1
2=1+1
3=1+1+1
4=1+1+1+1
5=put 5 link piece and remove other 1+1+1+1 (4) single pieces
6=5+1
......

72=put 72 links and remove 40+20+10+5+1+1+1+1
....
81=72+5+1+1+1+1
82=72+10


....
and so on upto 151 links

my answer :

5 + 1 + 10 + 1 + 20 + 1 + 50 + 1 + 62

--->>4 cuts

it is the same with the moneytary