A king asks a learned man to visit his palace, to which the learned man responds:
“I will come some day next month, but I will not tell you on which day. Further, you must give me gold in grams equal to the date on which I come.”
In preparation for the visit, the king demands that his jeweler make gold rings of 1 to 31 grams. The wise jeweler made only 5 rings.
What are their weights?
a possible solution? 1, 2, 4, 8 and 16 grams. Please correct if you find this to be wrong.
Why?
We want to create the numbers from 1-31 by adding up only 5 numbers.
we do need 1.
we might need 2.
we can create 3 from 2 and 1. (1+2=3)
we cannot create 4 from 1 and 2 so we need to use 4.
we can create 5 from 1 and 4 (1+4)
etc.
if we repeat this we can arrive to the number 15 using only 1, 2, 4, 8
Now we can stop since we know that 16+15=31. That means we can create all remaining numbers from 17 to 31 by adding 16+ all the numbers from 1-15
1
2
3 (1+2)
4
5 (4+1)
6 (4+2)
7 (4+2+1)
8
9 (8+1)
10 (8+2)
11 (8+2+1)
12 (8+4)
13 (8+4+1)
14 (8+4+2)
15 (8+4+2+1)
16
17 (16+1)
18 (16+2)
31 (16+15) or (8+4+2+1)
as king has to give the gold in grams having weight of date.so man probability to visit the palace is last 5 days of month.so wise jeweler made only 5 rings of weight 31,30,29,28,27 grams.
The gold bars would be of weight 1,2,4,8,16.
This puzzle is only an extension to “7 day 7 gm gold bar puzzle”
15 Pirates
————-
7 gold coins for the 7 pirates that will get nothing and 93 for the 15th
1,0,1,0,1,0,1,0,1,0,1,0,1,0,93
25 Pirates
————-
12 gold coins for the 12 pirates that will get nothng and 88 for the 25th
1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,88
This is the answer I guess…
I have also searched for more such puzzles… here is the another variant of this https://youtu.be/214sCqmKlPQ
