Brain Teasers - Coins

Problem Definition

Coins

Situation:
Imagine, we are sitting together at a perfectly round table. We both have an infinite pile of quarters. These are the rules of the game: “We'll take turns putting one quarter down on the table, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses."

Question:
Who should start in order to win, why and how does your strategy work?

Marbles

Situation:

There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times.

Question:

How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings.

Comments

Brain Teasers are short questions with difficult logical or creative answers. They are a good way to test your analytical skills and capacity to think out of the box. These short questions also show the interviewer your ability to elaborate on difficult tasks from the real world. Each Brain Teaser is supposed to be solved by the interviewee in about 5-10 minutes.

If the interviewee gets stuck in a brain teaser (i.e. spends more than 10 minutes), propose to go on to the next one.

Solution

Coins

You have to start. You place a quarter exactly in the center of the table. After that, whenever I put quarter on the table, mimic my placement on the opposite side of the table. If I have a place to place a quarter, so will you. I will run out of places to put a quarter before you do.

Marbles

Place 3 marbles on each tray.

• If the first weighing doesn't balance, remove all the marbles from the lighter side, and place one marble on each tray from the heavier tray. The heavier side is the 1.1 ounce marble, but if they balance, then the marble from the heavier tray from the first weighing that was not weighed in the second weighing is the heavier one.
• If the marbles balance on the first weighing, remove the marbles from the trays, and place 2 of the remaining not weighted marbles on the trays, one on each tray. If one is heavier, it is the heavier marble, but if they balance, the remaining not weighted marble is the heavier one.