Logic game «Which is larger? Which is smaller?»

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This is a logic game about comparing values. You’ll see two mathematical expressions on the screen, and the task is simple: choose the one that’s larger or smaller (depending on the question). The expressions vary: fractions, decimals, percentages, powers, roots, and mixed expressions. As the level goes up, the game doesn’t become “harder” so much as it becomes more devious: the gap between options shrinks, look-alike formats appear, and your brain is more likely to try to solve it on intuition.

🎮 How to play

The mechanics are as short and clear as possible:

  • the level is shown at the top;
  • below that is the question:
    • Which is larger? → choose the option with the greater value;
    • Which is smaller? → choose the option with the smaller value;
  • the two options are buttons;
  • after you choose:
    • the correct one highlights in green;
    • the wrong one highlights in red;
  • if you make a mistake, you’ll get the option to restart the game from the beginning.

🧩 What kinds of expressions you’ll see

To make it clear what exactly is being compared, here are the types that work well for scaling difficulty by level.

1) Fractions

  • 1/2 vs 3/8
  • 5/6 vs 7/9
  • 11/20 vs 0.55 (when a fraction and a decimal are mixed)

Traps:

  • same denominator → easy;
  • different denominators → your brain starts guessing based on the top numbers;
  • a fraction “close to 1” like 9/10 is often overestimated.

2) Decimals

  • 0.7 vs 0.65
  • 1.05 vs 1.5
  • 0.099 vs 0.1

Traps:

  • 0.099 looks “almost 0.1,” but it’s smaller;
  • lots of digits after the decimal point → your brain drops focus.

3) Percentages

  • 40% vs 0.35
  • 125% vs 1.2
  • 5% vs 0.04

Traps:

  • people confuse 40% with 0.04 (a true classic);
  • percentages above 100% feel “weird,” even though it’s simply 1.25.

4) Powers

  • 2³ vs 3² (8 vs 9)
  • 5² vs 2⁵ (25 vs 32)
  • 3⁴ vs 10² (81 vs 100)

Traps:

  • the same digits look similar, but the values are different;
  • people often underestimate exponents—especially with 2 (2⁸ = 256).

5) Roots

  • √49 vs 7
  • √50 vs 7 (the root is slightly larger)
  • √2 vs 1.4

Traps:

  • many people automatically round √50 down to 7;
  • √2 is often “eyeballed” as 1.2–1.3, even though it’s about 1.414.

6) Mixed expressions

  • (2³)/3 vs 2.5
  • √80/4 vs 0.7
  • 3 + 1/4 vs 3.2
  • 1/3 + 1/6 vs 1/2

Traps:

  • parentheses → your brain ignores them;
  • division after a root/power → for an untrained eye, it’s harder to process quickly.

📈 How difficulty scales by level

  • Early levels: big differences (for example, 0.2 vs 0.8).
  • Mid levels: similar magnitudes (for example, 2/3 vs 0.65).
  • High levels: close values + mixed formats (for example, √50/7 vs 1.01).

You start losing right where you try to guess. If you push for speed without checking, the error rate shoots up—the same principle applies to the Raven intelligence test as well.

✅ What this game trains

This game is useful not because “math makes you smarter,” but because comparing quantities is a core skill in a ton of everyday and work tasks.

  • Attention to detail: the sign, the exponent, the fractional part, the order of operations.
  • Speed of evaluation: quickly tell what’s bigger/smaller without a calculator.
  • Impulse control: not clicking on the first feeling.
  • Resistance to cognitive errors: the brain loves rounding and “filling in the blanks.”
  • Numeracy: percentages, fractions, and decimals start feeling like the same thing—just in different clothing.

⚠️ The most common player mistakes

If you want to clear levels more consistently, here’s where most people lose:

  • percentages ↔ decimals: 7% = 0.07, not 0.7;
  • fractions by “eyeballing”: 3/7 and 2/5 look similar, but that’s 0.428… vs 0.4;
  • roots: √48 and √49 seem the same, but the difference is noticeable;
  • powers: 3³ (27) often “feels” like 3² (9);
  • extra zeros: 0.50 = 0.5, but it looks “bigger.”

🛠️ Practical tips

You don’t need to “solve” anything here—you need to evaluate quickly.

Quick conversions

  • percentages → divide by 100
    65% → 0.65
  • fractions → estimate roughly
    3/4 ≈ 0.75, 2/3 ≈ 0.666, 1/3 ≈ 0.333
  • roots: keep anchor values
    √49 = 7, √64 = 8, √81 = 9
  • powers: anchors help here too
    2⁸ = 256, 3⁴ = 81, 5² = 25, 10² = 100

How to compare fractions without calculating (if you want to be faster)

  • If the denominators are the same → the one with the larger numerator is bigger.
  • If the numerators are the same → the one with the smaller denominator is bigger.
  • If everything differs → estimate in decimals, or compare to benchmarks like 1/2, 1, etc.

🧩 Who it’s for

  • Anyone who enjoys short logic challenges.
  • Anyone who wants to get more comfortable with percentages/fractions/decimals.
  • School and university students as a quick training tool.
  • Adults who want to stop making silly mistakes in simple comparisons.

🔁 Why it’s addictive

Because it’s fast and it keeps handing you a tiny challenge: today you cruise through fractions, and tomorrow you suddenly get caught on 0.099 vs 0.1. And that’s normal—the whole point is to notice where your brain starts cutting corners.