Logic and number words

Swap every letter for the number it stands for

HintThe values are given at the start — trade the symbols in first.

The whyOnce A = 2 and B = 5 become plain numbers, the sum is ordinary arithmetic. Copy carefully — a mis-copied value wrecks a correct method.

No — work strictly left to right, in the order written

HintSchool habits mislead you here — take the sum exactly as it comes.

The whyIn class, multiplying would come before adding; in these puzzles each step is applied as you meet it. Here 2 + 3 × 4 means 5 × 4 = 20, not 14.

Follow the sentence step by step from the given number

HintTreat it like a recipe — one instruction at a time, in order.

The whyWrite the running total down after every instruction; holding it in your head is where slips happen.

2 and 3

HintTwins for the first word; triplets for the second.

The why"Treble" appears far less often than "double" in everyday talk, which is exactly why papers use it. These little words carry the whole instruction.

Divide it by two

HintShare it into a pair of equal parts and keep one.

The whyHalving 18 gives 9. Watch for chains: "double it, then halve it" lands you back where you began.

Take the smaller away from the larger

HintIt measures the gap, so the answer is never negative.

The whyThe difference between 4 and 9 is 5. It is a subtraction in disguise — but always the small one from the big one.

The same relation links them in every worked example

HintTwo finished sets show the trick — find what both have in common, then reuse it.

The whyTry the simple relations first: add the outside pair, find their difference, or multiply them — perhaps then halving or doubling. Whatever fits BOTH examples is the rule to apply to the third.

The full order of everyone involved

HintPlacing just two people is not enough — the statements pin down the whole line-up.

The whyThe right order is the only one that fits every statement at once. If two different orders both fit, re-read — you have missed a clue.

Rule out the impossible until one arrangement is left

HintWork like a detective — cross off whatever the clues forbid.

The whyCheck every possibility against every clue rather than leaping at the first fit. The answer is the arrangement nothing forbids.

Add them together

HintPlus, in disguise.

The whyThe sum of 7 and 5 is 12. Do not confuse it with the product, which multiplies them instead.

It stops you forgetting a value part-way through

HintYour memory is the weak link — put the swap on paper where you can see it.

The whyLetters and numbers look nothing alike, so the swap itself is easy. Holding four of them in mind while you calculate is not. Write first, then work.

Give it as a letter if the question asks for one

HintCheck the wording at the end — symbols in, symbols out.

The whyA perfectly correct number can still score nothing when a letter was wanted. Papers usually say so in the instruction line, which is easy to skim past.

Numbers

HintEach one is a disguise for a value you were given at the top.

The whyThey carry no meaning of their own here. Once each has been replaced, nothing about the calculation is unusual apart from the order you work in.

Multiply them together

HintNot adding — this word means the times operation.

The whyThe product of 6 and 4 is 24. It is the partner of "sum", and muddling the two is one of the commonest slips in these questions.

Divide it by four

HintHalve, then halve again.

The whyA quarter of 20 is 5. Getting there in two easy steps is quicker under time pressure than setting out a division, and much harder to slip on.

add and subtract

HintOne word piles things up; the other measures a gap.

The whyPapers rarely use the plain words. Working out which operation a phrase is really asking for is most of the job in these questions.

They follow on one after another with no gaps

HintThink of house numbers along a street, counted in turn.

The whyConsecutive numbers rise by one each time: 7, 8, 9. Some questions ask for consecutive even numbers instead, which rise by two — read the wording closely.

Work out the rule from the finished examples

HintTwo complete sets are there to be decoded before you touch the third.

The whyResist starting on the unfinished set. The rule is the whole puzzle; once you hold it, filling the gap takes a moment.

Test it on the second finished set as well

HintA pattern that fits only one example may be a coincidence.

The whyOne set can often be explained several ways. The rule that survives both of them is almost certainly the one the question intends.

Turn each one into a short note or mark

HintWords take up room in your head; symbols on paper do not.

The whyA tick, a cross or an arrow captures a statement in a second and can be scanned again instantly. Re-reading whole sentences is what runs the clock down.

Their order, but not where either sits overall

HintYou learn who comes above whom — nothing yet about the whole line-up.

The whyA single comparison places two people next to each other and says nothing more. Only when the comparisons overlap does a full ranking appear.

All of them

HintNot most, not nearly — every single clue has to hold at once.

The whyChildren often stop as soon as the answer they expected appears. Checking the clues you have not used yet costs seconds and catches a near miss.

Recording what each clue rules out

HintCrossing off is easier to keep track of than holding possibilities in mind.

The whyRows for the people, columns for the things, and a cross in every box a clue forbids. Whatever is left standing at the end has to be the answer.

Yes — it removes a possibility and narrows the answer

HintKnowing where something cannot go tells you nearly as much as knowing where it does.

The whyNegative clues do the heavy lifting in these puzzles. Treat each one as a cross on your grid rather than as an unhelpful sentence.