Tech companies try to keep interview questions secret so prospective employees can’t prepare answers in advance. Applicants can regain power by sharing their interview experiences publicly on sites like Glassdoor and CareerCup. As a result, a forum originally intended to help career hopefuls navigate the job market has become a WikiLeaks for puzzle lovers. This week, I’ll be decrypting Bezos’ files and delivering them directly to your browser window, with free shipping, of course.
According to an article on CareerCup, our first dilemma came from the software engineer interview. It has a neat premise: mark faces on blank dice to achieve a given goal, but if you solve it too quickly, I’ve added two bonus puzzles that also explore blank dice.
Did you miss last week’s puzzle? check it out here, and find its solution at the bottom of today’s article. If you haven’t solved last week’s question yet, be careful not to read too far into it!
Puzzle #44: Blank Dice
Amazon Interview Question: If you rolled two typical dice and added their results, you would get a number between 2 and 12. You will only get 2, while 7 will appear frequently). Let’s say you have a regular die and a blank die (a small cube with no numbers on it). Mark blank dice with some subset of numbers 0, 1, 2, 3, 4, 5, 6 This way when you roll two dice, all the sums come from 1 to 12 is equally possible. You must mark each side of the blank die, and the numbers can be repeated.
bonus question Regarding blank dice, courtesy of Dmitry Kamenetsky: Given two blank dice A and B, label them once (without repetition) with the numbers 1 to 12, so that when you roll the dice, the probability of A being rolled is higher than the probability of B For 50% B has a 50% chance of rolling higher than A.
Label three Use the blank dice with numbers 1 to 18 once each (without repetition) so that when you roll the dice, each die has an equal chance of being the highest die.
Although these may seem like a tedious exercise in trial and error, they all have very intuitive solutions. I found the last problem particularly satisfying, but you have to solve the smaller cases first to solve it.
I’ll be back on Monday with answers and new puzzles. Do you know a cool puzzle that you think should be featured here? Leave me a message on X @JackPMurtagh or email me gizmodopuzzle@gmail.com
Solution to Puzzle #43: Anarchy Tic-Tac-Toe
Did you know how to beat me last week? Tic Tac Toe Variations? The first player can always force the win as follows. Thanks to Kari Roth for emailing the perfect solution with diagram. Kari wrote:
The difference with this variation is that you’re not actually trying to hit a triple, but instead trying to force the opposing player to hit a double with the third spot open.
Great insight. This is how Player One wins.
Start from the center. The sign doesn’t matter, so let’s say you start with X. I have to place an O, and there are only two options: corner elements or edge elements (it doesn’t matter which corner or edge because the board is symmetrical).
If I select a corner cell, then you will place an O in the opposite corner:
Now that I’m in Zugwang, the word means that every legal move puts me at a disadvantage. My best move was to pass, but the rules dictated that I had to move. No matter which cell I select and which symbol I place in it, I will open a trifecta for you.
Instead, if I place an O on one edge in the first step, you would follow a similar strategy and place an O on the opposite edge:
Here, the only way I can avoid letting you win on the next round is to place an O in the remaining edge cell. You will mirror it again and put me in zugzwang:
All actions are failures for me. Therefore, the first player can always force victory in Anarchy Tic-Tac-Toe by opening in the center and then mimicking their opponent’s moves until they have a chance to win.
