Oxford Computing toolkit

A variable

HintIn algebra the same idea wears a letter such as x; in code it wears a name such as score.

The whyIn maths a letter usually stands for one unknown number that never moves during the question. In code the same box is written to over and over: score = score + 1 means 'work out the right-hand side, then put the result back in the box'. Reading = as 'becomes' rather than 'equals' is the biggest single step from Year 7 algebra into programming, and the Blockly tasks in the younger age groups are built on it.

The remainder

HintIt is the bit that will not fit into any whole group — three sweets shared between two children leaves one.

The whyEven means the leftover is 0, odd means it is 1. The test costs one step however huge the number, which is why so many coding tasks hide an odd-or-even question inside them.

multiplied

HintThe two counts do not go together by addition — think of rows and columns in a rectangle of chairs.

The whyFive rows of four chairs is twenty chairs, not nine, and a loop inside a loop behaves the same way: an outer loop of 5 wrapping an inner loop of 4 performs 20 inner steps. This is why nesting makes a program slow so quickly — three nested loops over a hundred items each is a million steps, and a timed round will not wait for it.

A bubble sort

HintThe slowest of the classic ordering methods, and the first one most people are taught.

The whyIt makes pass after pass along the list, comparing item 1 with item 2, item 2 with item 3, and so on, swapping whenever a pair is the wrong way round; after each pass the largest remaining item has reached its place. Easy to write under pressure but slow — a hundred items can need thousands of comparisons. Every competition language already has a much faster built-in ordering method, and knowing when to reach for it is part of the skill.

first

HintThe across-then-up order is the same one you met for x and y; think of walking into a room before climbing the stairs.

The whyCoordinates are (across, up), so (3, 1) is three across and one up while (1, 3) is somewhere else entirely. Screen grids add one twist: many put (0, 0) at the top-left corner and count downwards, so a larger second number means lower down the screen. Check which convention a task uses before you move anything.

factorial

HintName the operation, not its value: a single word ending in -ial.

The why5! is 120, and it grows terrifyingly fast — 10! passes three million and 13! passes six billion. That is why a program that tries every possible order of a list is hopeless beyond about ten items, and why a task that looks like "try all the arrangements" almost always wants a cleverer idea instead.

8

HintIt is a power of two, and it is how many switches an old-fashioned text character needed.

The whyA byte holds 2⁸ = 256 different patterns, enough for every letter, digit and punctuation mark in plain English text. Larger units keep doubling in powers of two, which is why memory sizes run 512, 1024, 2048 rather than in round hundreds.

A brute-force search

HintTwo words: no cleverness at all, just raw effort until something works.

The whyThis approach is honest and always right, which makes it a fine first answer — but only when the number of options is small. Ten items can be arranged in 3,628,800 ways and a computer will chew through that happily; twenty items has more arrangements than a person could count in a lifetime. The skill is estimating the size of the job before writing it, then looking for a rule that skips most of it.

ten; two; sixteen

HintFingers, then switches, then a short-hand that squeezes long rows of switches into far fewer symbols.

The whyBase ten uses the digits 0–9 because we have ten fingers. Base two uses 0 and 1 because a switch is on or off. The third — hexadecimal — adds A to F so that a group of four bits becomes one symbol, which is why a colour on a web page is written like #FF8800. All three are the same numbers wearing different clothes.

An off-by-one error

HintThink of the posts along a fence: there is always one more post than there are panels.

The whyComputers usually number from 0 and people from 1, and the gap between those two habits is where this bug lives. Ask two questions before running any loop: does it start at 0 or at 1, and does it stop at the last value or just before it? Writing out the first two and last two steps by hand catches nearly every one.

A top Bebras result

HintIt is decided by how you did in the autumn computational-thinking challenge, not by applying.

The whyThe Oxford University Computing Challenge is run by the Raspberry Pi Foundation in partnership with the University of Oxford, and invitations go to roughly the top tenth of UK Bebras entrants. Bebras therefore does double duty: worth entering for its own sake, and the only door through to this. There are four age groups spanning ages 10 to 18, and everything is done online in school under a teacher's supervision, with answers marked automatically.

Write working code

HintBebras asks what a set of steps would produce; here you must build the steps and let a machine run them.

The whyYou do not describe a method here, you implement it, and it is tested automatically — so a nearly-right idea scores nothing. The two younger age groups work in Blockly, a drag-together block language, while the older groups may use a text language such as Python. Turning a Bebras answer into a small working program is the most direct preparation there is.