Logic and number words

Swap every letter for the number it stands for

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

为什么Once 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

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

为什么In 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

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

为什么Write the running total down after every instruction; holding it in your head is where slips happen.

2 and 3

提示Twins for the first word; triplets for the second.

为什么"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

提示Share it into a pair of equal parts and keep one.

为什么Halving 18 gives 9. Watch for chains: "double it, then halve it" lands you back where you began.

Take the smaller away from the larger

提示It measures the gap, so the answer is never negative.

为什么The 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

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

为什么Try 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

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

为什么The 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

提示Work like a detective — cross off whatever the clues forbid.

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

Add them together

提示Plus, in disguise.

为什么The 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

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

为什么Letters 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

提示Check the wording at the end — symbols in, symbols out.

为什么A 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

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

为什么They 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

提示Not adding — this word means the times operation.

为什么The 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

提示Halve, then halve again.

为什么A 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

提示One word piles things up; the other measures a gap.

为什么Papers 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

提示Think of house numbers along a street, counted in turn.

为什么Consecutive 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

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

为什么Resist 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

提示A pattern that fits only one example may be a coincidence.

为什么One 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

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

为什么A 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

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

为什么A 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

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

为什么Children 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

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

为什么Rows 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

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

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