Poisoned Wine Puzzle Answer: 10 Testers, 1,000 Bottles [Solved]

The poisoned wine puzzle answer is 10 testers, one round, and binary numbers. Label the bottles 1 to 1,000 in binary. Give each tester one binary place. After one round, read who is affected as 1 and who is not as 0. That 10-bit pattern is the number of the poisoned bottle.

Here is the puzzle in full. You have 1,000 bottles of wine, and exactly one bottle is poisoned. With 10 testers, you get only one round of testing. No second round is possible after waiting for the result. Still, you must find the poisoned bottle after that single round. At first, the numbers look hopeless. Or can 10 testers point to one bottle?

Yes, they can. The trick is not to divide the bottles into 10 groups. Instead, you must turn each tester into a digit. One tester alone tells you almost nothing. Ten testers together give you 1,024 different patterns. That is more than enough for 1,000 bottles. That, in one sentence, is the poisoned wine puzzle answer.

How the Poisoned Wine Puzzle Answer Works

Start with binary numbers. In binary, each place is worth twice the place to its right. The places, from right to left, are worth 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512. So a 10-bit number can stand for any whole number from 0 to 1,023. That range covers all 1,000 bottles, with room to spare.

Next, number the bottles from 1 to 1,000. Then write each bottle number in 10-bit binary. For example, bottle 1 is 0000000001, bottle 2 is 0000000010, and bottle 1,000 is 1111101000. In addition, each bottle now has its own 10-bit code, and no two bottles share a code.

Then assign one tester to each bit place. Tester 1 takes the rightmost bit, worth 1. After that, keep going in that order until Tester 10, who takes the leftmost bit, worth 512.

Now comes the tasting plan. Each tester takes a small sip from every bottle that has a 1 in his bit place. In contrast, he skips every bottle that has a 0 in his bit place. So Tester 1 sips from every odd-numbered bottle. In short, each bottle sends its sips to a different set of testers. Consequently, that set is exactly the set of 1 bits in its binary code.

After the round, read the result as a binary number. If a tester is affected, write 1 for his place. Otherwise, write 0. Then read the 10 bits from Tester 10 down to Tester 1. Finally, that number is the poisoned bottle. As a result, one round gives you the full answer.

A Small Example First: Poisoned Wine Puzzle Answer With 8 Bottles

It helps to shrink the puzzle first. Suppose you have 8 bottles, numbered 0 to 7, and 3 testers: A worth 4, B worth 2, and C worth 1. Now write each bottle number in 3-bit binary.

Bottle	Binary	Who sips
0	000	Nobody
1	001	C
2	010	B
3	011	B, C
4	100	A
5	101	A, C
6	110	A, B
7	111	A, B, C

Now suppose A and C are affected, but B is not. Write 1 for A, 0 for B, and 1 for C. As a result, that gives 101 in binary, which is 5 in decimal. So bottle 5 is poisoned. In addition, each affected set points to one bottle only, so the answer is certain.

The Poisoned Wine Puzzle Answer in 4 Steps

Step 1: Number the bottles. Write the numbers 1 to 1,000 on the bottles. Then convert each number to 10-bit binary. Finally, keep the same bit order for every bottle, from Tester 10 on the left to Tester 1 on the right.

Step 2: Assign the testers. Give Tester 1 the 1s place, Tester 2 the 2s place, and so on, up to Tester 10, who takes the 512s place.

Step 3: Run one round. Each tester sips from every bottle with a 1 in his place. He takes only a tiny sip from each bottle. In addition, the poison is strong enough that even a diluted sip counts, so a small sip is enough for the test.

Step 4: Read the pattern. After the waiting time, list the testers in order, from Tester 10 to Tester 1. Write 1 for each affected tester and 0 for each unaffected tester. Then convert that binary number to decimal. Finally, that decimal number is the poisoned bottle.

Worked Example: Poisoned Wine Puzzle Answer, Bottle 297

Suppose Testers 1, 4, 6, and 9 are affected. No other tester is affected. Next, build the pattern from Tester 10 down to Tester 1.

Tester	10	9	8	7	6	5	4	3	2	1
Value	512	256	128	64	32	16	8	4	2	1
Affected?	No	Yes	No	No	Yes	No	Yes	No	No	Yes
Bit	0	1	0	0	1	0	1	0	0	1

Add the values for the affected testers: 256 plus 32 plus 8 plus 1 equals 297. So bottle 297 is poisoned. In binary, 297 is 0100101001, which matches the pattern above. This worked example shows the poisoned wine puzzle answer in action.

Try one more case. If only Tester 10 is affected, the pattern is 1000000000. As a result, that is 512 in decimal, so bottle 512 is poisoned. However, if no tester is affected, the pattern is all zeros. That case cannot happen here, because exactly one bottle is poisoned.

Why 10 Testers Are Enough, and 9 Are Not

Count the patterns. One tester gives 2 patterns. In addition, two testers give 4 patterns. In general, n testers give 2 to the power n patterns. So 9 testers give only 512 patterns, which is far short of 1,000 bottles. However, 10 testers give 1,024 patterns, which covers 1,000 bottles with 24 patterns to spare. Therefore 10 is the smallest number that works, and that is why the poisoned wine puzzle answer is 10, not 9.

The Trap Most Candidates Fall Into

Most candidates start by splitting the bottles into groups. They give 100 bottles to each tester and plan to narrow it down. However, that plan fails at once, because one round gives only one result per tester. As a result, you still have 100 suspects left, and you have no round left to test them.

Another common trap is to test bottles one by one. That plan needs 999 tests in the worst case, which is far too slow. In contrast, the poisoned wine puzzle answer avoids that trap by testing all bottles at once, with each tester carrying one bit of information.

Watch out for one more detail. The sips must stay separate by tester, not mixed into one shared cup. Otherwise, a shared cup would tell you only that some bottle is poisoned, not which one.

What the Interviewer Is Testing in the Poisoned Wine Puzzle Answer

First, the interviewer tests whether you can encode information. The puzzle is not really about wine at all. It is about turning a bottle number into a pattern, and then reading that pattern back.

Second, the interviewer tests whether you can count patterns. Many candidates guess 10 testers by luck, but they cannot explain why 9 testers fail. The strong answer states the 2 to the power n rule and shows that 2 to the power 10 equals 1,024.

Third, the interviewer tests whether you can handle a one-shot constraint. In real work, you often get only one round of data before a decision. So the interviewer wants a plan that works the first time, with no second chance.

Finally, the interviewer tests clarity under pressure. A clear candidate starts with the answer, then explains the binary plan, then proves that 10 is minimal. So lead with the answer, keep the bit order fixed, and walk through one worked example.

This puzzle is reported as a Goldman Sachs puzzle-round question, in a test-strip form with 1,000 bottles and 10 strips, and it also appears in wider lists, such as this interview puzzle list. The solution above is original.

Try This Next

If you liked this puzzle, try the Egg Drop Puzzle next. It also gives you a limited number of tries, but you must find the breaking floor with the fewest drops. Then try the 25 Horses Puzzle, where 7 races find the 3 fastest horses with no stopwatch.

Frequently Asked Questions

Why does binary work here?

Binary works because each tester gives one yes or no result. Ten yes or no results make 1,024 patterns. Each bottle gets one pattern, so the pattern identifies the bottle. In short, the poisoned wine puzzle answer is binary encoding.

What if two bottles were poisoned?

Then this plan would fail. Two poisoned bottles would blend their patterns into one mixed pattern. So the plan rests on the stated fact that exactly one bottle is poisoned.

What is the smallest number of testers for 500 bottles?

Nine testers would do it. Nine testers give 512 patterns, which covers 500 bottles. Eight testers give only 256 patterns, so eight testers are not enough.