Bebras puzzles don't test facts you can look up — they test a handful of thinking habits that keep reappearing, dressed up in different stories each time. Once your child recognises the habit underneath the story, the puzzle gets much easier. Here are the ones worth knowing, explained without any computing jargon.

If you haven't read it yet, our full guide to the Bebras Challenge covers what it is, who runs it, and how to enter. This article goes one level deeper: the actual ideas the puzzles are built from.

A quick honest note on scope — this list is drawn from our own twelve-card Bebras flashcard deck, not from Bebras' full question archive (which isn't published as past papers; the puzzles are interactive and sat online only). So treat what follows as a solid grounding in the ideas that recur most, not an exhaustive checklist.

Algorithms: a set of steps that works every time

An algorithm is a precise list of steps that solves a problem when followed exactly — nothing more mysterious than that. A recipe is an algorithm. So is a knitting pattern, or a set of directions from the station to school. What makes something count as an algorithm is that a follower with no imagination still gets the right result, purely by doing exactly what it says — which is exactly why a computer can run one, and exactly why Bebras loves testing them. A typical puzzle either hands your child an algorithm (a robot's instruction list, a rule for shading squares) and asks what it produces, or hands them a result and asks which algorithm made it.

The habit that goes with this concept is tracing: working through the steps by hand, one at a time, rather than reading the instructions once and guessing at the outcome. Bebras puzzles are written to punish skimming — they reward a child who keeps a finger on the current position and does exactly what each step says.

The three building blocks: sequence, selection, repetition

Every algorithm ever written — however complicated — is built from just three kinds of step:

  • Sequence — one step, then the next. The default; nothing clever, just doing things in order.
  • Selection — a yes/no test that picks one of two paths. "If the tile is black, turn left; otherwise carry on."
  • Repetition — the same block of steps runs several times over. "Repeat four times" or "keep going until you reach the wall."

Spotting which one a puzzle is really testing tells your child how to trace it. A puzzle full of "if" statements is a selection puzzle — the trick is following the right branch. A puzzle about something happening "every third square" is a repetition puzzle — the trick is counting correctly.

Binary: how a computer counts in two digits

Ordinary numbers are base 10 — each place going left is worth ten times as much as the one before (1, 10, 100, 1000…). Binary is base 2 — each place going left is worth double the one before (1, 2, 4, 8, 16, 32…), and every digit can only be a 0 or a 1.

So the binary number 1011 doesn't mean "one thousand and eleven" — it means 8 + 0 + 2 + 1 = 11. Each digit is really a switch that's either on or off, and the value is just the sum of the place values that are switched on. This matters for Bebras because computers store everything this way, and puzzles about light bulbs, flags, or coins arranged in a row are very often binary in disguise, even when the word "binary" never appears.

A useful companion fact: with four binary digits, you can make exactly 16 different patterns (from 0000 up to 1111), because each digit doubles the possibilities — 2 × 2 × 2 × 2 = 16. Every extra digit doubles the count again, which is why so many Bebras answers land neatly on a power of 2.

Decomposition: taking a big problem apart

A Bebras puzzle can look enormous on the page — twelve friends, three buses, a page of seating rules. Decomposition is the computer scientist's answer to that: split a big problem into smaller ones you can actually check.

In practice that means: sort out bus 1 completely before thinking about bus 2. Deal with the seating rule before the luggage rule. Small problems have small, checkable answers, and the big answer is just those pieces put back together. Decomposition is one of the four classic "computational thinking" habits, alongside pattern spotting, abstraction (ignoring the details that don't matter), and algorithm design.

Binary search: halving your way to the answer

Imagine you have to guess a secret number between 1 and 100, and the only question you're allowed to ask is "is it bigger than…?" What's the smallest number of questions that's guaranteed to work, however unlucky you are?

The answer is 7 — not by guessing 1, 2, 3 in order (which could take a hundred tries), but by asking about the middle of whatever range is left each time. Ask "bigger than 50?" and half the possibilities vanish whatever the answer is: 100 → 50 → 25 → 13 → 7 → 4 → 2 → 1 is seven halvings.

This is called binary search, and it's the reason a sorted list is so quick to search through — it's also why Bebras puzzles so often involve things arranged in order.

Graphs: dots, lines, and the shortest route

A node is a dot in a "dots and lines" diagram — also called a vertex. The lines joining nodes are called edges, and the whole picture is a graph (not the x–y axis kind — the network kind). Computer scientists draw towns-and-roads, people-and-friendships, and tasks-and-what-must-come-first as the same kind of picture, because one method works for all of them.

A classic Bebras puzzle shows towns joined by roads, each labelled with a length in kilometres, and asks for the shortest route from school to the swimming pool. The trap is picking the route with the fewest roads — but one long motorway can easily outweigh three short lanes. The reliable method is to add up each route's actual lengths and pick the smallest total (the idea behind Dijkstra's algorithm — the method a sat-nav uses).

Parity and invariants: what a move can never change

A cup starts the right way up. You flip it over, one flip at a time, and stop after seven flips. Which way up is it?

You don't need to track every flip individually — you only need to know whether the total number of flips is odd or even, because every pair of flips cancels out. Seven is odd, so the cup ends upside down. This is called parity, and it's an example of an invariant — something a sequence of moves can never change, or changes in a completely predictable way.

Bebras puzzles about switching lights on and off, swapping cards, or hopping between squares are very often settled in a single line by parity, however many moves the puzzle describes.

Systematic listing: counting without missing or repeating

If you have three different letters and want to know how many different orders they can be arranged in, the reliable method isn't writing codes down at random until nothing new comes to mind — you can never be sure you haven't missed one or repeated one that way.

The reliable method is listing systematically: fix the first letter, then list every way the rest can go, in a fixed order — every code starting with A, then every one starting with B, then C. That guarantees you've found every arrangement and none twice. For three letters, each of the three starting choices leaves two ways to arrange what's left, so 3 × 2 × 1 = 6 orders in total.

This habit — an organised list rather than a hopeful guess — is what wins Bebras counting puzzles.

Putting it together

None of these ideas needs a computer to understand. They're all things a child can reason through with a pencil and a clear head: trace it step by step, spot which of the three building blocks is at work, remember binary is just doubling, break the big problem into small ones, halve your way to an answer, look for what never changes, and list things in order rather than guessing.

For where children typically go wrong on each of these ideas, see common Bebras mistakes and misconceptions. And for why a maths tutor is the one explaining all this, how Bebras thinking connects to KS3 maths explains the overlap.

FAQ

Do I need to understand computing to help my child prepare for Bebras?

No. Every concept Bebras tests — algorithms, binary, decomposition, systematic listing — can be explained in plain English, and this article does exactly that. None of it requires you to have ever written a line of code yourself.

Is this list everything Bebras could possibly ask about?

No — it's the concepts covered by our own Bebras flashcard deck, which draws on twelve cards. Bebras' real question bank is much larger and run by the Raspberry Pi Foundation, so treat this as a solid grounding in the recurring ideas, not an exhaustive syllabus.

Is computational thinking a separate subject from maths?

Not really, at KS3. It overlaps heavily with skills your child already practises in maths — systematic listing, number patterns, place value, and logical reasoning. We explore that connection in a separate article.