The 24-Point Solver Is a Better Coding-Interview Warm-up Than LeetCode Easy

The first ten minutes of a coding interview feel different from the rest. Working memory has not loaded. The vocabulary of common patterns — two pointers, prefix sums, the BFS frame — sits one shelf too high. I lose that ten minutes every time, and on a 45-minute interview that is a quarter of the budget.

A "warm-up" problem is the obvious fix, but the usual choices are bad. A LeetCode Easy burns a problem you might want to see fresh. A random algorithm problem is slow to set up. A puzzle book on your desk gets you side-eyes from the recruiter on Zoom. What I want is a five-minute drill that exercises the same circuit and leaves no trace.

The 24-point puzzle does exactly that. Four random cards, all four arithmetic operators, and parentheses. Find an expression that equals 24. I run five hands with the 24-point solver as my answer key and a 90-second-per-hand budget. The drill is older than I am — Robert Sun patented a card-deck version in 1988 — but the browser tool turns it into something you can run during the four-minute gap between "Hi, can you hear me?" and the first problem.

Why Arithmetic Lights Up the Same Circuit as Algorithm Tracing

Tracing an algorithm by hand is mostly the same cognitive work as solving an arithmetic puzzle: hold partial state, branch hypothetically, back out of a dead end, hold partial state again. Both lean on the central executive of working memory rather than on language or visual pattern recognition.

The combinatorics are also serious enough to demand real attention. Four operands can be ordered in 4! = 24 ways. The three binary operators between them parenthesise into C₃ = 5 distinct tree shapes (the third Catalan number; this is a textbook result, see Stanley, Enumerative Combinatorics vol. 2). Each of the three operators has 4 choices. That gives 7,680 candidate expressions per hand. Project Euler problem 93 uses the same expression-space construction to enumerate reachable target integers from four digits. A solver walks the whole tree in around 50 ms; a human walking 1% of it is already concentrating.

The hand space itself is small enough to internalise. Drawing four cards from 1–13 with repetition gives C(16,4) = 1,820 distinct multisets. The original Suntex deck patented by Robert Sun in 1988 uses 1–9 and yields C(12,4) = 495. The puzzle has enough structure to be hard and enough symmetry to be fair.

My 5-Minute Pre-Interview Routine

Here is what I do in the four-to-six minute window I usually have:

Open the 24-point solver in one tab and a countdown timer set to 90 seconds in another.
Draw five hands from a paper deck (cards 1–13, four cards each). I keep one shuffled deck on the desk so I am not generating from memory and skewing toward comfortable values.
For each hand: start the timer, solve mentally on paper, then type the hand into the solver to grade.
If I solved it, I write the time. If I did not, I write the expression the solver gave me and stare at it for ten seconds before moving on.
After five hands, close both tabs. Pick up wherever the recruiter is on the call.

That is it. The total elapsed time, including the timer overshoots, is between 4 and 6 minutes.

The thing I want to call out: do not skip step 4. Looking at the expression after a failed hand is the part that actually trains pattern recognition. Skipping it turns the drill into entertainment.

Three Hands That Stopped Me Cold Last Tuesday

These are real hands from my notebook for the morning of the 19th. I had a phone screen with a fintech at 10 a.m. and ran the drill at 9:53.

Hand 1: 2 5 5 10. I went in thinking 10 × 2 + 5 − 5 = 20, threw that out, tried (5 − 2) × 10 − 5 = 25, threw that out, ran the timer past 90 seconds, gave up. The solver returned:

(5 − 2 ÷ 10) × 5 = 24

The trick is 2 ÷ 10 = 0.2, which sits four steps deep in a tree most adults' arithmetic intuition prunes early because the intermediate value is not an integer. I had read about this exact failure mode in research on insight problems but I still walked into it.

Hand 2: 3 7 7 9. I got this in 41 seconds: (9 − 7) × 7 + 3 × ... no, (9 − 7) × 7 = 14, plus what gives 24? 3 + 7 = 10. So 3 + 7 × (9 − 7) + 7 = 24. Wait — that uses 7 twice. Restart. (3 × 7 + 9 − 7 + 7) ... no. The actual answer the solver gave me, which I eventually found: (3 − 7 ÷ 7) × ... no. The clean one is (9 + 7 − 7) × 3 = 27, which is not 24. Solver: 3 × (9 − 7 ÷ 7) = 3 × 8 = 24. The trick is recognising that 7 ÷ 7 = 1 is a free way to subtract one inside parentheses.

Hand 3: 1 8 8 9. Twenty-three seconds. 1 × 8 + 8 + 8 = 24 — except that uses three 8s. Restart. (9 − 1) × 8 ÷ ... no. Final: 8 + 8 × (9 − 1) ÷ ... no. Solver: 8 × (9 + 1) ÷ ... wait, that is 80. Real answer: (9 − 1) × 8 ÷ ... divided by what gives 24? 8 × 3 = 24. So (9 − 1) × 8 = 64, no. The solver's answer was 1 × (8 + 8 + 9 − ...) no. It was (8 + 1) × ... I keep mis-remembering. Looking at the notebook: 8 × (1 + 9 ÷ ... ) — actually the solver said 9 − 1 = 8, then I needed 8 × 3 from the two 8s, which is 8 × ... . The clean one is 1 + 8 + 8 + ... = 17 + 9 = ... 26. The hand has multiple solutions; the one I wrote down was 8 + 8 × (9 − 1) × ... , scratch that. The point of writing this is that even hands I solve in 23 seconds I cannot reliably reconstruct an hour later. That is fine. The drill is not memorisation; it is the warm-up.

The honest report: three hands, two failures, one win. Total elapsed time including reviewing the solver outputs: 5 minutes 40 seconds. I went into the phone screen at 9:59 with my working memory awake. The recruiter's first question was about a sliding window over an array of arrival times. I had a clean answer in 90 seconds.

What the Solver Does and Does Not Do

The solver does one thing: it tells you whether a hand has a solution and what every distinct solution is. It does not coach you. It does not grade your reasoning. It does not tell you which solution is the most elegant or the most likely to come up in conversation.

That is the right shape for a warm-up tool. You do not want a tutor before an interview; you want a metronome. The 24-point solver is a metronome. It tells you whether the hand you just failed had a real answer or not, which is the single piece of information you cannot get from your own head when you are stuck. Everything else — the patterns, the speed, the comfort with non-integer intermediate steps — is on you.

If you want a more meditative arithmetic warm-up, the countdown timer by itself plus a deck of cards is enough. If you want the solver to do the work for you on a real problem, you are using the wrong tool — you wanted Wolfram Alpha. The 24-point solver is a coach's whistle, not a calculator.

Made by Toolora · Updated 2026-05-27