You are here

The 1000 Poisoned Wine Bottle Riddle

The 1000 Poisoned Wine Bottle Riddle Solution

Find the poisoned wine bottle from 1000 similar wine bottles gifted to you using 10 test strips that change color when a drop of poisoned wine falls on it.

The Poisoned Wine Bottle Riddle

You have 1000 bottles of wine. One is poisoned. You also have 10 test strips that can detect poison by changing its color with a drop of the poisoned wine on it. The poison takes an hour to show up on the strips. You need to find the poisoned bottle within an hour to save yourself from being poisoned. How do you do it?

Assume the 1 hour starts ticking just after you finish putting wine drops onto the strips.

Hint: First form the primary condition for successful identification of the poisoned bottle before thinking about the solution.


Solution to the 1000 Poisoned Wine Bottle Riddle

Stage 1: Forming the primary condition and strategy for successful identification of poisoned bottle

Primary condition: To test all the 1000 bottles using 10 test strips:

  • We need to identify only one bottle from the set of strips that changed color receiving wine drops from it. No two bottles should produce the same combination of strip results.

Form the strategy that would meet the primary condition:

  • Number the bottles from 1 to 1000.
  • Place the strips one after the other and mark position of each as 1 to 10 from right.
  • Devise a method of putting drops from a bottle to the strips occupying a unique combination of positions. No two bottles should deliver its drops to the same combination of strip positions.

This is the point of reasoning when the position of strips gains focal attention.

  • The only way to implement this strategy is to form a 10 position unique identifier for a bottle in which the strips in positions receiving drops from it are marked 1 with the rest 0.
  • This identifier will then form a 10 digit number with its digits 1 or 0 only.
  • Conclusion: Create a numbering scheme in which a 10 digit number with digits 1 or 0 corresponds to a number in the range 1 to 1000.

Stage 2: Discover how to form the winning numbering scheme

From your experience in daily calculations, you already know how numbers are formed.

For example, you know a randomly chosen number 1234 as a sum of an increasing series of numbers 0, 10, 100, 1000 starting from the right moving toward left, and each multiplied by the digit in a specific position.

Thus, 1234 = 1x1000 + 2x100 + 3x10 + 4x1.

Why 10? Because any position of the number may have one of the 10 values from 0 to 9. Right? This is the positional value of a number in this scheme used daily.

But what about the puzzle strips? How many values a strip position can take?

Revelation: Color of a test strip may remain either unchanged or will change into a specific color when poisoned. A strip can then have only two states 0 for unchanged and 1 for changed. This fits perfectly into our strategically arrived conclusion.

Extend the concept of forming the numbers such as 1234 to this new scheme:

  • Positional value is 2 multiplied by position number of times minus 1. Example, positional value of 5th position is 2x2x2x2 = 16.
  • Final value of a number: Sum of position number multiplied by positional value for each position. Example: 0000101101 = 0000 + 32 + 0 + 8 + 4 + 0 + 1 = 45.

Stage 3: Actions to find the poisoned bottle

First step: The bottles 1 to 1000 are marked using this new 10 digit numbering scheme:

1: 0000000001 : 000000000 + 1x1

2: 0000000010 : 00000000 + 1x2 + 0

3: 0000000011 : 00000000 + 1x2 + 1x1

.....

1000 : 1111101000 : 1x512 + 1x256 + 1x128 + 1x64 + 1x32 + 0 + 1x16 + 000.

Second step: Putting the drops from the 10 digit numbered bottles onto the strips at positions where the 10 digit number has 1.

Example: The 110th bottle is marked with 10 digit number 0001101110. Wine drops from this bottle are put onto the strips at positions: 2, 3, 4, 6 and 7 from right.

Third step: Waiting for 1 hour to know which strips have changed color.

Stage 4: Find the poisoned bottle from the strip positions that changed color

If strips in positions 1, 3, 4, 7 and 9 changed color, corresponding 10 digit number having 1s in positions 1, 4, 5, 7 and 9 must have received drops from the poisoned bottle.

The number is:

0101001101 => 0 + 256 + 0 + 64 + 0 + 0 + 8 + 4 + 0 + 1 = 333

Expanding the values, 256, 64, 8, 4 and 1 in terms of binary number system,

333 = 1x28 + 1x26 + 1x23 + 1x22 + 1x20, where 26 means 2 multiplied with itself 6 times, expressed in shorthand form mathematically,

Or, 333 = 1x2(9-1) + 1x2(7-1) + 1x2(4-1) + 1x2(3-1) + 1x2(1-1), where the first terms inside the brackets are positions of digit 1 in the 10-digit binary number, similar to decimal number system.

This is the way the numbers in the two-digit binary number system with 0 and 1 as digit values, are formed.

Solution: 333rd bottle contains the poisoned wine.

You have saved yourself from being poisoned.


Identifying the poisoned wine bottle by the method of binary number system and its equivalence to decimal numbers

identifying-poisoned-wine-bottle.png

This binary numbering scheme discovered by extending your idea about the numbers you use daily is the basis of the digital world today.


More puzzles to enjoy

From our large collection of interesting puzzles enjoy: Maze puzzles, Riddles, Mathematical puzzles, Logic puzzles, Number lock puzzles, Missing number puzzles, River crossing puzzles, Ball weighing puzzles and Matchstick puzzles.

You may also look at the full collection of puzzles at one place in the Challenging brain teasers with solutions: Long list.

Enjoy puzzle solving while learning problem solving techniques.