The Logical Reasoning section is 15 of the 50 questions in an IMO paper, and it needs no formulas at all — only a method for each question type. Here are the five that appear most.
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Compare the code with the original letter by letter and the rule appears at once.
🔤 Letter positions — write these down first
| A–G | H–N | O–U | V–Z |
|---|---|---|---|
| A1 B2 C3 D4 E5 F6 G7 | H8 I9 J10 K11 L12 M13 N14 | O15 P16 Q17 R18 S19 T20 U21 | V22 W23 X24 Y25 Z26 |
🔐 The three common codes
Shift. CAT → DBU means every letter moves forward by 1. So DOG → EPH.
Opposite letter. A↔Z, B↔Y, C↔X — the pair always adds to 27. So CAT → XZG.
Position numbers. RED → 18, 5, 4. Watch for +1 or ×2 applied on top of the position.
Check the shift on two letters, not one. If TEACHER is coded VGCEJGT, T→V is +2 and E→G is +2, so the rule is confirmed. Then CHILD → EJKNF.
Draw a picture. Do not try to hold these in your head.
👪 Untangling a relation
Read the sentence backwards, from the far end towards the speaker.
"The son of my father’s only son" — my father’s only son is me, so this is my son.
Draw men as squares and women as circles, and join them with lines as you go.
Directions. Facing north, a right turn takes you east; another right takes you south. Anticlockwise goes the other way: from east, a left turn faces you north. Sketch a compass in the corner of the sheet.
Distance questions are Pythagoras in disguise. Walk 3 km north and then 4 km east and you are 5 km from the start in a straight line — not 7 km.
Find the step between the terms — and if the steps differ, look at the steps of the steps.
➡️ Series to recognise
| Series | Rule | Next |
|---|---|---|
| 3, 6, 12, 24, … | double each time | 48 |
| 1, 4, 9, 16, … | the square numbers | 25 |
| 2, 6, 12, 20, 30, … | differences 4, 6, 8, 10 | 42 |
| 2, 3, 5, 7, 11, … | the prime numbers | 13 |
| 1, 1, 2, 3, 5, 8, … | add the two before it | 13 |
| AZ, BY, CX, … | forward from A, backward from Z | DW |
An analogy asks for the same relationship, not the same kind of word. Cat : Kitten :: Dog : Puppy is "adult to young". Read the first pair aloud as a full sentence, then apply that sentence to the second.
12 Olympiad reasoning questions. Write the alphabet out at the top of your rough sheet. 🍀
