Project Euler is a programming challenge site, similar to LeetCode or HackerRank, but the problems are generally more pure math or number theory rather than typical computer science algorithms. Project Euler is less about improving programming skills than about solving the problems, you only submit the answer to the problem, not the code used to get the answer.

I originally started Project Euler about a year ago to get better at Python. After two dozen or so problems, I kept thinking "I can't get the Python to work right, but I know exactly how I'd do this in Excel". Eventually I decided to see how far I could get using only Excel.

At first Excel more as intended, with giant columns of numbers and operations occurring in every cell, but the file quickly ballooned in size and was incredibly messy. So I then started trying to keep the solutions contained in one formula in one cell. This was a terrible idea and I don't recommend it, Excel can only multi thread calculations across multiple cells, not within a single cell. Often the only way I could cancel a calculation was to force close and reopen the file.

Each solution is entirely self-contained within a single cell (with the exception of those that require a data input). Project Euler states that every problem is able to be solved in less than one minute, I only had three problems that take longer than that (60, 72, and 88; each take 5-10 minutes), and most are essentially instant.

Overall it was a really fun challenge. I definitely improved as I went along and I would probably approach a lot of the early problems in a different way after finishing.

File

You can download the final spreadsheet with all formulas here.

Stats

• The longest formula comes in at 2,647 characters and features 82 functions and 61 lines, used in problem 75.
• The shortest was 25 characters, using 2 functions, for problem 10.
• REDUCE is used in 59 problems, LET and LAMBDA are used in 79, HSTACK/VSTACK is used in 45, however the most used function is probablySEQUENCE, used in a whopping 87 problems

Biggest Headaches

• Big numbers: Excel can't store more than 15 digits, and there are several problems with 50 or 100 digit numbers, or calculations like 99^99. I had to build custom digit-wise addition, multiplication, and exponentiation functions that store numbers as text to get around it.
• Recursion: Recursive LAMBDAs have a limit of ~6400 recursions, and that number goes down as you add variables. Fortunately, this only applies to each pure LAMBDA call, not to the built-in functions like REDUCE. Several problems are very easy with rudimentary recursion but quickly go over the recursion limit, which made it very challenging.
• Iteratively updating an array: There is no good way to do this, it requires rebuilding the array every single time. Essentially eliminates any dynamic programming approaches and makes for loops very slow

Interesting things I learned

• Excel is so bad at updating arrays that a lot of programming tips are just wrong when applied to Excel. For example, take the Sieve of Eratosthenes (explained below). I built a version of this in my file (sieve), and it works decently well for n <= 10,000, but slows down a lot after that and is basically unusable for n > 50,000. Conversely, my naive prime generator function (primeGen) calculates and counts the divisors for every odd number from 3 to SQRT(n), and it is exponentially faster than the sieve and works for n <= 500,000 in a reasonable time (possibly more, I didn't check higher n).

The Sieve of Eratosthenes efficiently finds all primes up to n by repeatedly marking multiples of each prime as non-prime, starting from 2. This avoids redundant checks and quickly filters out all composite numbers.

• The best way to do an OR operation on each element of 1D array is with MMULT. This vectorizes it and is much faster than MAP or XMATCH.
• REDUCE is easily the most powerful formula currently available in Excel and I used it for a vast majority of problems. It is the only iterative function that lets you access and modify the accumulated value, and can pass arrays as it's argument. It replaces For loops very easily, it can replace Do loops but not quite as easily, and can even do some limited recursion tasks. REDUCE can replace virtually any LAMBDA that doesn't use heavy recursion, you can use HSTACK to essentially pass arguments as different elements of a single array, including arguments of different dimensions.
• Some problems were actually easier in Excel than they would have been in a traditional programming language. Like problem 19, which asked how many Sundays fell on the first of the month in the 20th century; or problem 89, which involved numbers written in Roman numerals.

Disclaimers:

• I made very liberal use of ChatGPT/Gemini while making many of the formulas. While it almost never produces a working formula from scratch (and often claims its impossible), It is very good at improving formatting and variable names, and identifying what is causing errors. Basically any formula with indents was at least partially re-written by AI. For some reason I can't figure out, all the LLMs are convinced you can add comments into an excel formula, and they do it constantly.
• I personally built every single formula and function used while solving the 100 problems, with the exceptions of the sudoku solver in problem 96, which I copied from a post in this subreddit by u/Verochio; and the permutations and combinations generator I modified from this comment by u/Anonymous1378.
• Some problems require using data stored in .txt files, for nearly all of these I was able to copy and paste into one cell, with no other pre-manipulations of the data. For three problems, the txt data was too long to fit in one cell and I was forced to paste the data into cells on another sheet but did not do any other pre-processing.
• I did not count named functions as violating the one formula per problem constraint.