# Analytics Interview Puzzles

Author: Ipshita Chakraborty

In the last blog, we have discussed two analytics puzzles. Now, we want to share with you a list of puzzles.

Puzzle 3: 3 switches, 1 light puzzle
There are 3 light switches outside a room and the corresponding light bulbs inside the room. Standing in the hall, you cannot see whether the light bulbs inside are on or off. You can operate the switches in whatever way you want, as many times as you want.
You are allowed to go inside the room only once. How will you determine which of the light switches controls the light inside the room?

Puzzle 4: 2 ropes problem, measure 45 minutes
There are 2 identical ropes and a lighter. When each rope is lit, it takes an hour to burn completely from one end to another. Using these two ropes and the lighter, how would you exactly measure 45 minutes?

Puzzle 5:3 ants triangle puzzle
Suppose there is a triangle and there are 3 ants on each of its 3 vertices (or corners). Now the ants start walking along the sides of the triangle. What is the probability of a collision between any 2 or all of the ants?

Puzzle 6:9 Marbles Puzzle – Find Heaviest / Lightest
This is a commonly asked puzzle where a set of marbles or pennies are given, all but one weighing the same. A weighing scale is provided which will not give the exact weight of any item but two items (or groups of items) can be compared to determine if one is heavier or lighter than the other. The puzzle can ask the question in two different ways –
1. Finding the heaviest (or lightest) marble in 2 attempts OR
2. Determining the minimum number of weighing required to find the heaviest (or lightest) marble

Let’s work with a puzzle with a definite number of pennies to start with and generalize it to N later.

Sub-Puzzles:

Puzzle 1:

You are given 9 marbles, 8 of which weigh exactly the same, but one marble weighs less than the other 8. You also have a weighing scale. Determine the minimum number of attempts to find the lightest marble.

Puzzle 2:

There are n marbles which are of the same size except one which is heavy. What is the minimum number of times you have to weigh those marbles to find the heavy ball?

Puzzle 7:4 people on a rickety bridge
4 people need to cross a rickety bridge at night. They only have one torch among themselves. The bridge is only strong enough to support two people at a time. The 4 people take different times to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

Puzzle 8:25 horses, 5 tracks, finding fastest 3 horses
Suppose there are 25 horses and 5 tracks so that only 5 horses can run at the same time. You need to select the fastest 3 horses out of the 25. Given only this information, and given there is no stopwatch, what is the minimum number of races required to find the 3 fastest horses?

Puzzle 9:The 3 hats puzzle
3 men A, B and C are standing in a straight line in front of one another. A hat is out on each of their heads. They are told that each of these hats was selected from a group of five hats: two black hats and three white hats.
The first man, standing at the front of the line, can’t see either of the men behind him or their hats. The second man, in the middle, can see only the first man and his hat. The last man, at the rear, can see both other men and their hats.
None of the men can see the hat on his own head. They are asked to deduce its color. Some time goes by as the men ponder the puzzle in silence. Finally the first one, at the front of the line, makes an announcement: “My hat is white.”
He is correct. How did he come to this conclusion?