## Alchemical Reduction

### September 10, 2019

Today’s exercise is from the 2018 Advent of Code, Day 5:

You’ve managed to sneak in to the prototype suit manufacturing lab. The Elves are making decent progress, but are still struggling with the suit’s size reduction capabilities.

While the very latest in 1518 alchemical technology might have solved their problem eventually, you can do better. You scan the chemical composition of the suit’s material and discover that it is formed by extremely long polymers (one of which is available as your puzzle input).

The polymer is formed by smaller units which, when triggered, react with each other such that two adjacent units of the same type and opposite polarity are destroyed. Units’ types are represented by letters; units’ polarity is represented by capitalization. For instance, r and R are units with the same type but opposite polarity, whereas r and s are entirely different types and do not react.

For example:

– In aA, a and A react, leaving nothing behind.

– In abBA, bB destroys itself, leaving aA. As above, this then destroys itself, leaving nothing.

– In abAB, no two adjacent units are of the same type, and so nothing happens.

– In aabAAB, even though aa and AA are of the same type, their polarities match, and so nothing happens.

Now, consider a larger example, dabAcCaCBAcCcaDA:

dabAcCaCBAcCcaDA The first 'cC' is removed. dabAaCBAcCcaDA This creates 'Aa', which is removed. dabCBAcCcaDA Either 'cC' or 'Cc' are removed (the result is the same). dabCBAcaDA No further actions can be taken.After all possible reactions, the resulting polymer contains 10 units.

How many units remain after fully reacting the polymer you scanned?

Your task is to write a program that solves the alchemical reduction. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Semi-Primes

### September 6, 2019

We have on several occasions seen functions for generating the primes less than *n*. Sometimes, what you want instead of primes are *semi-primes*, numbers which are the product of two primes. For instance, the six semi-primes less than 25 are 2×3=6, 2×5=10, 2×7=14, 3×5=15, 3×7=21 and 2×11=22.

Your task is to write a function that makes a list of the semi-primes less than *n*; use it to discover the number of semi-primes less than 10,000. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Date Conversion

### September 3, 2019

Where I work, the accounting department does a survey of its vendors once a year, or every three years, or something, I’m not sure of the details. All of the vendors send CSV files with multiple rows, from a few rows to several hundred; each row contains 3 dates. Different vendors send dates in different formats: 9/3/19, 9-3-19, 09/03/2019, 3-SEP-19, “September 3, 2019” (quoted to protect the embedded comma), and even 09/03/2019T14:37:26.8493 (because every ten-thousandth of a second matters). That variety of formats caused problems for the accounting department, so they asked for help in reformatting the dates. Here is some sample data:

John,Smith,9/3/19,9-3-19,09/03/19,100 Sally,Jackson,3-SEP-19,"September 3, 2019",09/03/2019T14:37:26.8493,200

Your task is to write a program to convert dates from a variety of formats to the standard MM/DD/YYYY format. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Numbers With 3 Divisors

### August 30, 2019

I saw this question on Stack Overflow a few days ago; it’s a well-known problem in number theory:

For a given number

n, how many numbers less thannhave exactly 3 divisors?

Your task is to write a program that counts the numbers less than *n* that have exactly 3 divisors, and use it to find the result when *n* is one billion. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Powers Of 3

### August 27, 2019

This problem appeared on a beginning-programmers discussion list:

How can I determine if a number

nis a power of 3?

Your task is to write a program to determine if a number is a power of 3. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Sexy Primes

### August 23, 2019

A *sexy prime* is a prime number *p* for which *p* + 6 is also prime. Such primes are called sexy because the Latin word for six is *sex*.

Your task is to write a program that counts the sexy primes between one billion and two billion. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Sum Distinct Items

### August 20, 2019

We have an interview question today:

In a list of integers, find the sum of the integers that appear only once. For instance, in the list [4 2 3 1 7 4 2 7 1 7 5], the integers 1, 2, 4 and 7 appear more than once, so they are excluded from the sum, and the correct anser is 3 + 5 = 8.

Your task is to write a program to find the sum of the distinct integers in a list. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Last Man Standing

### August 16, 2019

Today’s exercise is a fun task for a lazy summer Friday:

Given a circular array

Xof positive integers and a starting indexkof the array, delete the element atkand jumpX[k] steps in the circular array. Repeat until only a single element remains. Find the last remaining element.

For example, with array 6 2 3 1 4 7 5 and *k* = 3, the last man standing is 3, computed as shown below, with the item to be deleted at each step marked with brackets and the list rotated at each step to bring the new head of the list to the front:

6 2 3 [1] 4 7 5 4 [7] 5 6 2 3 5 6 [2] 3 4 3 4 [5] 6 6 3 [4] [6] 3 3

Your task is to write a program to find the last remaining element. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## Round To 5

### August 13, 2019

Every morning when I drive to work the highway signs display commute information: 7 minutes to Manchester Road, 11 minutes to Olive Blvd, speed ahead 55 mph. That’s little comfort when I’m sitting still on the highway. The “speed ahead” calculation is always rounded to the nearest 5 mph; the Department of Transportation takes a bunch of speed readings from sensors buried in the pavement and averages them.

Your task is to take a list of speed readings and average them to the nearest 5 mph. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

## A Triangular Sequence

### August 9, 2019

Consider the triangle:

1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 ...

When the triangle is flattened, it produces the sequence (1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 …).

Your task is to write a program to generate the flattened sequence, and a second program to calculate the nth item in the sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.