No, this isn’t magic or a circus show. It’s a toolbox that, well-trained, wins you precious seconds on every problem — and in an olympiad, seconds are points.
Multiplying Fast: Break the Number Apart
Instead of multiplying straight through, split it into easy parts. 47 × 8 makes your head spin at once, but (50 × 8) − (3 × 8) = 400 − 24 = 376 you solve almost without thinking.
Squares Near Round Numbers
(a + b)(a − b) = a² − b² is your best friend here. Need 97²? Think of it as (100 − 3)² = 100² − 2(100)(3) + 3² = 10000 − 600 + 9 = 9409. With practice, this comes out in seconds.
Divisibility, Without Doing the Division
- By 3 or 9: add the digits. If that sum is divisible, so is the number.
- By 4: just look at the last two digits.
- By 11: alternately subtract the digits (right to left) and check whether the result is a multiple of 11.
This isn’t trivia — in number theory, checking divisibility fast saves you real minutes.
Percentages Without a Calculator
10% is “move the decimal point.” From there, everything builds: 5% is half of 10%, 15% is 10% + 5%, 20% is double 10%. Combining these four, you can get almost any common percentage without writing out a single long calculation.
“Mental math doesn’t replace understanding the problem. But once you know what to do, the arithmetic shouldn’t be what slows you down.”
How Do You Train This?
- Practice it on its own, outside of a full problem — like a warm-up before the real training.
- Start slow and deliberate, speed comes on its own with repetition, not the other way around.
- Use it in everyday life — calculating change, a discount on a sale, whatever. The more you use it, the less it feels like a “trick” and the more it becomes a reflex.
None of these tricks will solve an olympiad problem for you on their own. But combined with problem-solving heuristics and avoiding the typical mistakes under pressure, they’re the difference between finishing the exam with time to spare or getting stuck halfway through.