🔢CountUp: The Running Total Maths Game That Sharpens Mental Arithmetic

Mental arithmetic is a use-it-or-lose-it skill. When was the last time you actually added something up in your head instead of reaching for your phone? If the honest answer is "a while ago", CountUp might be for you.

CountUp is a free maths puzzle game with the tagline "A Running Total Game". It's available in your browser right now at mento.co.uk/countup, plus on iPhone, iPad, and Android. The idea is simple: you get a grid of number tiles, you get a target, and you have to combine tiles with operators to reach it. But there's one twist that changes everything.

The Running Total Rule

Normal maths uses BODMAS (or PEMDAS if you're American) — multiplication and division happen before addition and subtraction, regardless of the order you wrote things down. CountUp doesn't work like that.

In CountUp, calculations run left to right, like an old pocket calculator. Each operation is applied to the running total immediately.

That means 2 + 8 × 3 doesn't equal 26. It equals 30.

Here's why: you start with 2, add 8 to get 10, then multiply that running total by 3 to get 30. The multiplication doesn't skip back and grab just the 8 — it applies to wherever you currently are.

Once you've got that in your head, the game opens up completely.

An Example Board

Here's a real Normal-difficulty grid (4×3, twelve tiles) with a target of 476:

20  21  74  28
37  27   9   3
38  49  34  53

476 looks intimidating. But once you start scanning for factor pairs — numbers that multiply to something near the target — paths start appearing.

37 − 20 × 28 = 476

Running total: start at 37, subtract 20 to get 17, multiply by 28 to get 476. Clean three-tile solution — and because all tiles are double-digit, this one also ticks off the "10+" achievement.

38 − 21 × 28 = 476

Same structure: 38 minus 21 is 17, times 28 is 476. A completely different pair of tiles arrives at the exact same intermediate value. This is the kind of coincidence that makes CountUp grids feel like they have hidden architecture.

3 + 9 × 38 + 20 = 476

Running total: 3 + 9 = 12, × 38 = 456, + 20 = 476. Four tiles, no subtraction — which means it also qualifies for the "Stay Positive" achievement. In standard BODMAS, 3 + 9 × 38 + 20 equals 365 (because 9 × 38 = 342 is computed first). In CountUp it's 476. This is the gap that catches people out until they internalise the rule.

20 + 27 × 9 + 53 = 476

20 + 27 = 47, × 9 = 423, + 53 = 476. Four different tiles, same target. Another subtraction-free route.

49 − 37 × 38 + 20 = 476

49 − 37 = 12, × 38 = 456, + 20 = 476. Note that this arrives at 456 the same way 3 + 9 × 38 does — both produce 12 before the multiplication. Once you spot that 12 × 38 = 456 is useful, you start hunting for every pair of tiles that produces 12.

That's five solutions, and we haven't touched 74, 21 (except in solution 2), 27, 28, 34, or 53 in most of them. There are more routes in that grid. Finding them all is the actual game.

Each of these counts as a separate solution. The game tracks every unique combination you find, and you need to find multiple paths through the same board to unlock achievements.

Nine Achievements Per Board

This is where CountUp gets its replay value. Every grid has nine achievements to unlock, and they push you to approach the same numbers in completely different ways:

• Solved — reach the target at all (the first one to tick off)
• Five Ways — find five distinct solutions to the same grid
• Three — solve it using three tiles or fewer
• Even / Odd — solve it with an even or odd number of tiles
• Divide & Conquer — include a division somewhere in your solution
• Smooth Operators — use all four operators (+ − × ÷) in one equation
• Stay Positive — reach the target without using any subtraction
• 10+ — solve it using only double-digit tiles

Some of these feel easy at first. Finding five unique solutions to the same board, or hitting the target using only double-digit numbers, forces you to think about the grid in ways you wouldn't naturally try. The "Smooth Operators" one — fitting all four operators into a single chain — can turn a simple board into a proper mental workout.

Grid Sizes

Four difficulty levels, four grid sizes:

Difficulty	Grid	Tiles
Hard	3×3	9
Normal	4×3	12
Easy	4×4	16
Beginner	5×4	20

Counterintuitively, smaller grids can be harder. With nine tiles and a tricky target, the number of possible paths is limited, and finding five different solutions — let alone one using all four operators — can be genuinely difficult. The larger grids give you more tiles to work with, so finding solutions is easier, even if the grid itself looks more intimidating.

Why It Works as a Mental Arithmetic Trainer

CountUp isn't a drill. There are no timed tables tests or fill-in-the-blank worksheets. But it does force you to do mental arithmetic constantly, because that's the only way to play.

To find solutions efficiently, you start doing things like:

• Scanning for factor pairs of the target (if the target is 30, you're looking for tiles like 5 and 6, or 3 and 10)
• Spotting combinations where two tiles add or subtract to a useful number ("if I add those two together I get 12, and 12 × ... hmm")
• Working backwards from the target ("I need to end on 30, so if I multiply at the end by 5 I need to be at 6 before that step")

That last one — working backwards — is genuinely useful mental maths, and CountUp nudges you into it naturally.

The no-time-pressure design matters here. You can sit with a grid for as long as you like. There's no timer ticking down and no penalty for thinking slowly. That makes it feel much less stressful than a mental maths app that's trying to quiz you.

Who It's For

CountUp works for quite a range of people:

Kids learning maths — it makes arithmetic feel like a puzzle rather than homework, and the running total rule is actually a great introduction to the idea that how you evaluate an expression matters.

Adults who want to stay sharp — if you feel like your mental maths has got a bit rusty in the era of calculator phones, a few grids a day is a low-effort way to keep it ticking.

Puzzle fans — if you enjoy number puzzles like Countdown (the TV show) or KenKen, the "find multiple solutions" mechanic will click immediately.

Teachers — the game is free, offline, and appropriate for all ages. The browser version means no install needed.

Download or Play in Your Browser

CountUp is free with no ads and no data collection. You can try it in your browser without installing anything — just pick a difficulty and start playing. The app versions are on the App Store and Google Play if you want to play offline or track your achievements over time.

Fair warning: the "just one more grid" effect is real.