Egg Drop Puzzle Answer: 14 Drops [Solved]

Answer: 14 drops. The egg drop puzzle answer is 14 drops in the worst case. Drop the first egg from floor 14, then 27, then 39, and keep shrinking the gap by one floor each time. If the first egg breaks, walk up floor by floor with the second egg. No strategy can guarantee an answer in fewer than 14 drops.

You have two identical eggs and a 100 floor building. The task is to find the highest floor from which an egg can drop without breaking. Call that floor the critical floor. If an egg survives a drop from a floor, then it will survive every lower floor. If an egg breaks at a floor, then it will break at every higher floor. The goal is to find the critical floor with the fewest drops in the worst case, not in the lucky case.

The Egg Drop Puzzle, Stated Clearly

Google recruiters made this puzzle famous, and it still shows up in tech and finance interviews because it tests how a candidate handles a scarce resource. You start with two eggs. The egg drop puzzle answer rewards candidates who protect the second egg until the end. A surviving egg can be reused. A broken egg is gone. Once both eggs are broken, the game is over, so the second egg must never be wasted on a wild guess.

First, note the two edge cases. The critical floor can be 0, which means even floor 1 breaks an egg. It can also be 100, which means an egg survives a drop from the top floor. A correct method must handle both ends, and it must work for every critical floor in between.

How the Egg Drop Puzzle Answer Works

The winning idea is simple once you see it. Each time the first egg survives, you have spent one drop, so you can afford one fewer linear check later. Therefore the gaps between first egg drops should shrink by one each time. Start with a gap of 14, then 13, then 12, and so on.

The drop sequence, floor by floor

Here is the full drop sequence for the first egg:

First egg drop number	Floor	If the egg breaks here
1	14	Check floors 1 to 13 with the second egg: at most 13 more drops, 14 in total
2	27	Check floors 15 to 26 with the second egg: at most 12 more drops, 14 in total
3	39	Check floors 28 to 38 with the second egg: at most 11 more drops, 14 in total
4	50	Check floors 40 to 49 with the second egg: at most 10 more drops, 14 in total
5	60	Check floors 51 to 59 with the second egg: at most 9 more drops, 14 in total
6	69	Check floors 61 to 68 with the second egg: at most 8 more drops, 14 in total
7	77	Check floors 70 to 76 with the second egg: at most 7 more drops, 14 in total
8	84	Check floors 78 to 83 with the second egg: at most 6 more drops, 14 in total
9	90	Check floors 85 to 89 with the second egg: at most 5 more drops, 14 in total
10	95	Check floors 91 to 94 with the second egg: at most 4 more drops, 14 in total
11	99	Check floors 96 to 98 with the second egg: at most 3 more drops, 14 in total
12	100	No linear check is needed: the critical floor is 99 if it breaks, or 100 if it survives

Two worked examples

Next, work through one full example. Suppose the critical floor is 73. Drop from 14, 27, 39, 50, 60, and 69, and the egg survives each time. Then drop from 77, and the egg breaks. Now you know the critical floor lies between 70 and 76. Drop the second egg from 70, 71, 72, and 73, and it survives each time. Then drop it from 74, and it breaks. So the critical floor is 73, found in 12 drops.

Now try the worst case. Suppose the critical floor is 38. Drop from 14 and 27, and the egg survives. Drop from 39, and the egg breaks. Then check floors 28 through 38 with the second egg, one by one. All 11 survive, and the break at 39 confirms the answer. That is 3 first egg drops plus 11 second egg drops, which is 14 in total.

Why the Egg Drop Puzzle Answer Is 14, Not 10

Many candidates suggest a fixed gap of 10 floors. That plan drops from 10, 20, 30, and so on. However, if the first egg breaks at floor 100, then you have already used 10 drops, and you still need up to 9 linear checks for floors 91 to 99. So the worst case is 19 drops, not 10. A fixed gap looks tidy, but it wastes drops in exactly the case that matters most.

By contrast, the shrinking gap plan balances the two risks. A break early costs many linear checks, so the first gap must be large. A break late costs few linear checks, because fewer drops remain. In short, the gap shrinks because each surviving drop buys less room for error.

Finally, here is the proof that 14 is the minimum. With 14 drops, the most floors you can cover is 14 plus 13 plus 12, all the way down to 1. That sum is 105, which covers a 100 floor building. With only 13 drops, the most floors you can cover is 13 plus 12, all the way down to 1. That sum is 91, which falls short of 100. So 13 drops can never be enough, and 14 drops are enough. That is the whole argument, and it is the part interviewers most want to hear.

Three Traps That Catch Candidates

First, do not confuse the average case with the worst case. A fixed gap of 10 feels fast when the egg breaks early, but the interview asks for a guarantee. Always answer for the worst case, and say so out loud.

Second, do not spend the second egg on a jump. Once the first egg breaks, the only safe move is floor by floor. Any jump with the last egg risks breaking it before the answer is pinned down, and then the puzzle is lost.

Third, do not forget the edge cases. State at the start that the critical floor can be 0 or 100. That one sentence shows the interviewer that you checked the boundaries before you started counting.

What the Interviewer Is Testing

This puzzle is not really about eggs. It tests whether you can trade a scarce resource against worst case cost, and whether you can prove that your plan is optimal. The shrinking gap shows structured thinking. The triangular number sum, 14 plus 13 down to 1 equals 105, shows that you can prove a lower bound, not just guess a method. And the worked examples show that you can run your own plan to the end without hand waving.

For interview practice, say the egg drop puzzle answer first, then the plan, then the proof. That order keeps the interviewer oriented, and it mirrors how a clear engineer explains a solution under pressure.

Try Another Puzzle Next

If you liked this one, try the 25 Horses Puzzle Answer: Fastest 3 in 7 Races. It uses the same kind of elimination logic, but with races instead of drops, and the final race is a genuine surprise.

Frequently Asked Questions

What is the egg drop puzzle answer?

The egg drop puzzle answer is 14 drops in the worst case, using two eggs and a 100 floor building, with first egg drops at 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, and 100.

Why does the gap shrink by one each time?

Each surviving first egg drop uses up one drop from the budget, so the next gap must be one floor smaller to keep the worst case total at 14.

Can 13 drops ever work for 100 floors?

No. With 13 drops you can cover at most 91 floors, because 13 plus 12 down to 1 equals 91. Since the building has 100 floors, 13 drops are not enough.

What happens if the first egg breaks at floor 14?

Then check floors 1 to 13 with the second egg, one by one. The critical floor is the last floor that survives, or 0 if floor 1 breaks.