I like to keep my brain sharp by working on programming puzzlers. On off weeks I'm going to start posting programming puzzlers I've collected over the years. Hopefully you'll find them as entertaining as I do.
Problem 1
Let’s play with narrowing down a random number generator evenly.
Assume you are given a random-number generation function called Rand4() that generates a random number from 1 to 4 inclusively (i.e. 1, 2, 3, or 4) with equal probability and eventually even distribution. That is, you may get several 3s in a row, but over the long term the number of 1s, 2s, 3s, and 4s are the same.
Given the Rand4() function, create a Rand3() function that also has equal probability and distribution for numbers from 1 to 3 inclusively.
Problem 2
Now, let’s go the other way and expand!
Given a Rand5() that generates a random number from 1 to 5 inclusively with equal probability and eventually even distribution, create a Rand7() function that also has equal probability and distribution for numbers from 1 to 7 inclusively.
Note
Remember! The primary focus on both of these we want to preserve the equal probability and even distribution. That said, we also want to preserve the “randomness” as well. Of course, efficiency is preferable as well, but not at the cost of these other traits.
Spoiler Alert!
Fair Warning: there may be discussion of the problem and potential solutions posted in the comments below. Read at your own risk.