Logic for wine drinking!!

1000 wine bottles were ordered for a feast by a king. 4 days before the feast, a person was caught mixing poison in a wine bottle, it is known that poison is present in only one wine bottle. King has 10 expendable workers, which he can order to drink wine. Now by using only those 10 people how can you separate that poisonous wine bottle, given that it takes 3 days for poison to kill a person.

#Combinatorics

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I am familiar with this puzzle. The solution uses binary mapping.

Flag each bottle with an unique $10$ digit binary representation, As $1000 < 2^{10}$ , such representation is possible. For example,

$1^{st} \; \textrm{bottle will be flagged as 0000000001}$ $2^{nd} \; \textrm{bottle will be flagged as 0000000010}$ $3^{rd} \; \textrm{bottle will be flagged as 0000000011}$ $.$ $.$ $1000^{th} \; \textrm{bottle will be flagged as 1111101000}$

Let the workers be $A_1, A_2, A_3, A_4, A_5, A_6, A_7, A_8, A_9$ and $A_{10}$

And each binary representation represents an unique drinking combination. For example the $3$ rd bottle represents,

$\begin{Vmatrix} A_1 & A_2 & A_3 & A_4 & A_5 & A_6 & A_7 & A_8 & A_9 & A_{10}\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \end{Vmatrix}$

means only $A_9$ and $A_{10}$ will drink the 3rd bottle.

Another example, 1000 th bottle represents

$\begin{Vmatrix} A_1 & A_2 & A_3 & A_4 & A_5 & A_6 & A_7 & A_8 & A_9 & A_{10}\\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \end{Vmatrix}$ means $A_1, A_2, A_3, A_4, A_5$ and $A_7$ will drink the 1000 th bottle.

And after $3$ days we can uniquely determine which bottle is poisoned, observing which workers die. For example, If $A_1, A_2, A_3, A_4, A_6, A_8$ and $A_{10}$ die after $4$ days, this will represent,

$\begin{Vmatrix} A_1 & A_2 & A_3 & A_4 & A_5 & A_6 & A_7 & A_8 & A_9 & A_{10}\\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \end{Vmatrix}$

means the $1111010101_2 = 981_{10}$ th bottle is poisoned

tasmeem reza - 6 years, 4 months ago

can't we ask the person who was mixing the poison????? just having fun!

parth tandon - 6 years, 8 months ago

hehe, nice try, i should mention that all the bottles look exactly identical! so even he wont be able to tell that

Vivek Bhagat - 6 years, 8 months ago

1000 has 10 digits of binner. So we can separate that poisonous bottle with 10 person

hanif adzkiya - 6 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$