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Wrong Answers Are The Hard Part

A devlog by Neeraj Kotwani, who builds every game on Elipar.

Reflex Math is the simplest-sounding game on this site. A sum appears, four buttons, tap the right one before the timer runs out, three lives. The whole thing fits in one file.

The part that took the actual thought is the three wrong answers.

The distractors are the difficulty

If the answer is 47 and the other options are 3, 112 and 8, there is no arithmetic in this game at all. You glance at the magnitude and tap. If the options are 46, 47, 48 and 49, you have to compute it exactly — and then read four nearly-identical numbers under time pressure, which is a different and more annoying skill.

So the wrong answers are generated around the correct one with a spread that is part of the difficulty curve, and the direction it moves is the counterintuitive bit.

The spread widens as you get better. At a low streak the options sit close together, so a near-miss mental slip is caught. By a high streak they are further apart.

That looks backwards until you remember what else is happening. The timer is shrinking at the same time — from 4.6 seconds down toward 1.6. At 1.6 seconds, four numbers within one of each other is not a test of arithmetic, it is a test of reading small digits fast. Widening the spread as the clock tightens keeps the game about the sum.

Two dials moving in opposite directions, so the thing being tested stays constant. That is the design, and I would not have got there by tuning one number at a time.

Three ramps, all capped

Difficulty rides on three independent things, and every one of them has a ceiling.

Operators unlock by streak. Addition only to begin with. Subtraction joins at a streak of four, multiplication at nine. A fresh player is never handed a times table in the first ten seconds.

The number range grows, then stops. It scales with streak and caps at 26 — because past that the sums stop being mental arithmetic and start being written arithmetic, which nobody is doing with a 1.6-second timer.

The timer shrinks exponentially, with a floor. A decay of 0.9 per streak point is gentle early and tightens later, and it never goes below 1.6 seconds.

The caps are the load-bearing part. An uncapped ramp in a game like this does not produce a hard game, it produces a game that becomes impossible at a fixed point and therefore has a maximum score everyone converges on. Capping all three means skill keeps mattering.

There is also a guaranteed gentle opener: the first problem of every run is small single digits regardless of anything else, so a fresh run cannot start with a gut-punch. Cheap, and it decides whether somebody plays a second round.

Subtraction never goes negative, and that is deliberate

When the operator is subtraction, the second operand is drawn to be no larger than the first. The answer is always positive.

That is a real constraint rather than an oversight. This is the Education category's arithmetic game, aimed at a general audience including children who have not met negative numbers. A game that tests negative results needs to teach them first, and a timed multiple-choice quiz is the worst possible place to introduce a concept.

Multiplication is held to single digits for the same reason — it is a times-table check, not a long-multiplication check.

The formula outlived the game

This was the first reflex game here, and its three constants — the starting duration, the floor, the decay — plus its streak multiplier have since been lifted verbatim into three more games: the flag quiz, the whack-a-mole, and one other.

That is deliberate. Four games teaching a player four different senses of how fast a streak should pay would be worse than four games that feel like siblings. Each one adds whatever its own format needs — the whack-a-mole scales how many bugs are up at once, which a one-question-at-a-time quiz does not need — and leaves the shared curve alone.

It did produce one failure worth recording, in the whack-a-mole's test. I hand-typed an array of expected scores and it disagreed with the game: the multiplier steps up at a streak of five, not after it, and I had typed it one step late from memory of how the formula works rather than from the formula.

The fix was to go and read this game's source, since that is where the formula came from, rather than adjusting numbers until the test passed. If a formula exists in two places and the test disagrees with one of them, read the original.

Reflex Math is free in a browser, no account, no download. The wrong answers are wrong on purpose.

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