# Minimal palindromic base

What’s this? Two posts in one day? Well, writing a static blog generator can do that. 😄

Another easily phrased challenge:

We have a simple little problem today: Given an integer n > 2, find the minimum b > 1 for which n base b is a palindrome.

Minimal Palindromic Base via Programming Praxis

# Number words

Today’s five minute post brought to you via Programming Praxis / Career Cup:

Given a positive integer, return all the ways that the integer can be represented by letters using the mapping 1 -> A, 2 -> B, …, 26 -> Z. For instance, the number 1234 can be represented by the words ABCD, AWD and LCD.

# Call stack bracket matcher

Five minute post from Programming Praxis:

Write a function to return true/false after looking at a string. Examples of strings that pass:

{}, [], (), a(b)c, abc[d], a(b)c{d[e]}

Examples of strings that don’t pass:

{], (], a(b]c, abc[d}, a(b)c{d[e}]

# Caesar cipher

Here’s a 5 minute1 coding challenge from Programming Praxis:

A caeser cipher, named after Julius Caesar, who either invented the cipher or was an early user of it, is a simple substitution cipher in which letters are substituted at a fixed distance along the alphabet, which cycles; children’s magic decoder rings implement a caesar cipher. Non-alphabetic characters are passed unchanged. For instance, the plaintext PROGRAMMINGPRAXIS is rendered as the ciphertext SURJUDPPLQJSUDALV with a shift of 3 positions.

– Source: Wikipedia, public domain

# Smallest consecutive four-factor composites

Another post from Programming Praxis, from this past Tuesday:

The smallest pair of consecutive natural numbers that each have two distinct prime factors are 14 = 2 * 7 and 15 = 3 * 5. The smallest triplet of consecutive natural numbers that each have three distinct prime factors are 644 = 2^2 * 7 * 23, 645 = 3 * 5 * 43 and 646 = 2 * 17 * 19. What is the smallest set of four consecutive natural numbers that each have four distinct prime factors?

# Visualizing the Monkey Grid

I’m a bit behind the times, but this post from Programming Praxis intrigued me enough that I kept it in my todo list for rather a while. So let’s get around to it.

I’ll just copy the description straight from the Programming Praxis website (although there are at least two previous version:):

There is a monkey which can walk around on a planar grid. The monkey can move one space at a time left, right, up or down. That is, from (x, y) the monkey can go to (x+1, y), (x-1, y), (x, y+1), and (x, y-1). Points where the sum of the digits of the absolute value of the x coordinate plus the sum of the digits of the absolute value of the y coordinate are lesser than or equal to 19 are accessible to the monkey. For example, the point (59, 79) is inaccessible because 5 + 9 + 7 + 9 = 30, which is greater than 19. Another example: the point (-5, -7) is accessible because abs(-5) + abs(-7) = 5 + 7 = 12, which is less than 19. How many points can the monkey access if it starts at (0, 0), including (0, 0) itself?

# Swap list nodes

It’s been rather a while since I’ve worked out a Programming Praxis problem, but they posted a new one yesterday, so now seems as good a time as any. The problem is relatively simple:

Given a linked list, swap the kth node from the head of the list with the kth node from the end of the list.

Since all lists in Scheme are linked lists, that part seems easy enough. To make the problem a little more interesting however, I’m going to work it out in a purely functional manner: no mutation.

# Cyclic equality

In today’s post from Programming Praxis, the goal is to check if two cyclic lists are equal. So if you have the cycles ↻(1 2 3 4 5) and ↻(3 4 5 1 2), they’re equal. Likewise, ↻(1 2 2 1) and ↻(2 1 1 2) are equal. But ↻(1 2 3 4) and ↻(1 2 3 5) are not since they have different elements while ↻(1 1 1) and ↻(1 1 1 1) aren’t since they have different elements.

# Approximating Pi with Buffon's Needle

I’m a bit late for Pi Day, but Programming Praxis had a neat problem on Friday that I wanted to check out:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?