Question :-
Once upon a time in ancient times there was a king who was very fond of
wines. He had a huge cellar, which had 1000 different varieties of wine all
in different caskets (1000 caskets in all). In the adjoining kingdom there
was a queen who was envious of the king’s huge wine collection. After some
time when she could not bear it any more she conspired to kill her by
poisoning all his wine caskets. So she one sentry to poison all the
caskets, but no sooner had the sentry poisoned only one wine casket that he
was caught and killed by the Royal guards. Now the king had a major problem
in his hand so as to identify the right casket, which he gave to the
Minister. Now the position had two peculiar qualities
Anyone who takes even one drop of poison will die.
But, he will die only after one month.
The king also gave the Minister 10 prisoners who could be used as
tasters, cause there lives was of no consequence to the king of kingdom for
that matter, and the Minister was given one month to find the poisoned
casket. Is it possible for the Minister to find out in one month? If so
how? If not then how many months are required?
My solution :-
This can be done in one month
Think the solution in binary
ok first i wanna ask u a question :- how many bits are needed to represent
the number 1000 ?
yeah u r right -> 10 bits
so here is the solution
let if any prisoner alive it mean it doesnt die and it will be represented
by 1 else if he dies then he will be represented by 0
number the prisoners from 0-9 with 0 the right most (LSB)
now what will be binary representation of 0 ? 0000000000
so if 0th bottle is poisoned then all prisoners must die so taste the
0th(actually 1st) wine to all the prisoners.
what is binary representation of 1? 0000000001
so taste the 1st(actually 2nd) wine to all except the 0th prisoner.
for 2nd, all except 1st (considering 0th as lowest bit) one
and so on.............
so at the end if suppose 6th and 2nd prisoner(consider 0 min and 9 max) left
alive then answer will be :- 1*2^5+1*2^1 +1 (note:- here ^= power)
if anyone have more general solution pls let me know
*I hope this is useful :) :)*
--
**Regards
SAGAR PAREEK
COMPUTER SCIENCE AND ENGINEERING
NIT ALLAHABAD
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