Dropping Two Eggs Puzzle

You are given 2 identical eggs and a 100-floor building.

An egg dropped from the Nth floor or above will break.

But, it will not break if dropped from any floor below N.

How do you find N with the fewest number of drops for the worst case?

How high before they break?

How high before they break?


Drop the first egg from floors K1, K2, … Kz until it breaks on drop z.

Then drop the second egg from floor K[z-1]+1 and each floor above till it breaks when dropped from floor N.

Finding N takes z + N – K[z-1] drops.

If the first egg breaks on the second drop, it will take the same number of drops to find N if K1 = K2 + 1.

Generalize to K[i+1]=K[i]-1.

Starting at K1=14 would reach the 99th floor as the 11th drop of the first.

Worst case is 14 drops for N=14,27,39,50,60,69,77,84,90,95, and 99.

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Sorting Resistors Puzzle

An engineer ordered 9 boxes of 100-ohm resistors and a box of 110-ohm resistors.

All 10 boxes arrived with 10 resistors each,

but both the boxes and the resistors were unmarked.

The engineer needs to find which box has the 110-ohm resistors.

He has an ohm meter to measure resistance.

How can he find the 110 box with the fewest resistance measurements?

Which box has 110 ohms?

Which box has 110 ohms?



Label the boxes, “1”, “2”, …, “10.”

Connect in series, 1 from 1st box, 2 from 2nd, and so on till 10 from 10th box.

Measure the resistance (M) of this series of 55 resistors.

If all 55 were 100 ohms, then M = 100*(1+2+…+10)=5500.

We find the box of 110-ohm resisters from this one measurement as

Box = (M-5500)/10.

The measured resistance R will only be 10 ohms larger that 5500 if the first box contains 110-ohm resistors.

One measure of 55 resistors.

One measure of 55 resistors.

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Three Lights Puzzle

An electrician finds 3 switches that control 3 lights in a distant room.

He cannot see the lights from the room with the switches.

He needs to figure out which switch controls which light.

You can assume each switch controls only one light, and that each light/switch pair works correctly. (Light is on/off when switch is on/off.)

How can he find the answer in the fewest trips between the switches and the lights without help? 

Which switch, which light?

Which switch, which light?



Turn switch “1” on and leave it.

Leave switch “3” off.

Turn switch “2” on for a minute, then leave off.

Quickly go to the bulbs.

Label the on bulb “1”.

Label the off bulb that is still warm “2”.

Label the off bulb that is cold “3”.

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