Worker and gold wage

I had hired a worker to perform a job. He had to work for 15 days to finish my job. I was supposed to pay him with a fixed qualtity of gold every day. I had a long gold bar which had just enough gold to pay him for 15 days. (Assume that the bar was uniform throughout).

Now, I want to cut this bar only at 3 places and at the end of each day balances with each should be perfect.

For example, at the end of day 5, worker should have 5units of gold and I should have 10 units of gold. At the end of day 6, worker should have 7 6units of gold and I should have 8 units of gold.

Now any amount of interaction between the worker and me is allowed. (For example, I can take back a pice given to the worker yesterday and give him a new piece of gold today which covers all his wages to date.)

Now, where should I cut my bar assuming that it has 15 units marked on it?

hi,
i think u can cut at 1,2,4 and u can distrubute the gold on each day throughout the 15 days.pls do update f iam wrong

u assume thatu have 15mts of gold rod then u cutit at 1mt,3mt,7mt then u will be able to distribute

Here is the answer for your question:

Totally you have 15 units of gold.

So cut the gold bar in the following way.

1+2+4+8 (because only three cut available)

firstday = 1
second day = get back 1, give it to 2.
third day = 1 so 1+2 =3.
fourth day = get back 1 and 2, give it to 4.
.
.
.
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you can give it to him upto 15 days.

I think i eplained correctly....plz correct me if i am wrong.

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

Yes. Both of your answers is right.
Strange coincidence. The answer turns out to be multiplication series of 2 rather 2^x series...
(2^0, 2^1....)

Good work guys.

Cheers!
Kalayama