New year party celebration puzzle
Mr Andrew wants to have a party on new year eve i.e. 1st of Jan, where he will be serving his 512 barrels of wine. In the Christmas celebration, his enemies poisoned one of the barrels. The poison kills any man who drinks the wine in about 6 days.
A plant called Xtonix also get affected and killed by the poison in 6days and can be used to test the wine. Xtonix is very rare plant so very costly and limited, Mr Andrew decided to buy some Xtonix plant to test the poisoned barrel.
How can he identify the single poisoned barrel of wine?
What is the minimum number of plants needed for the same?
You need 9 plants to check.
he will mark the wine barrel from 1 to 512.
and plant also with number 1 to 9
then he will feed the plant number 1 with wine from barrels 1+3+5+7+……+511
plant number 2 with wine from 2+3+6+7+…..+511
plant number 3 with wine from 4+5+6+7+12+13+14+15+….+511.
plant number 4 with 8+9+10+11+12+13+14+15+…+511
plant 5 with 16+17+18+..+511
plant 6 with 32+33+34+…+511
plant 7 with 64+65+66+….+511
plant 8 with 128+129+…..+511
plant 9 with 256+257+……+511
Now checking witch plants die you can determine the which wine bottle contains poison
if plant 1,3,5,7,9,…. die then barrel 1 contain poison
if plant 2.3,7,… die then barrel 2 contain poison
and so on
and if all plants die the barrel 511 contains poison.
and if none of the plants die then barrel 512 contain poison
You require 9 plants to check.
Let us take the wine barrel and name them 1 to 512.
First take 511 wine barrels. Keep Barrel no 52 separately.
The Plant be A,B,C,D,E,F,G,H,I
Now convert the number 1 to 511 into binaries and form a table like below
Now take the 1st wine barrel. Look at its binary form. It has digit 1 at A. So put a drop of wine in Plant A.
Take 2nd wine barrel. It has digit 1 at B. So put a drop of wine at Plant B.
Take 3rd wine barrel. It has digit 1 at A and B. So put a drop of wine in both Plant A and Plant B.
Take 511th wine barrel. It has digit 1 in All A,B,C,D,E,F,G,H,I. So put 1 drop in all the plants.
Wait for 6 days.
Check how many plants died. If a plant dies, then make that as 1, if not 0.
For eg., Plant A,B,C,D dies.
Then the binary form is 000001111.
Convert it into Decimal.
The value will represent the wine bottle. In this case it is 15.
If none of the plant dies, then the poison is in 512th bottle.
If he uses 1 plant, it would take him a lot of days to find the poisoned barrel of wine.
In the worst case scenario, it would take 6*512=3072 days.
Which is about eight and a half years.
Andrew can theoretically accomplish this using a single plant, but he can’t celebrate the party with wine this year, it would take another 9 years.
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