Class 3 IMO Achievers Section HOTS Riddles with Visual Explanations (2x Marks)

In the SOF International Mathematics Olympiad, Questions 31 to 35 form the legendary Achievers Section. Unlike standard questions which test single-step direct computations, Achievers questions are multi-step puzzles requiring creative heuristics, reverse logic, and spatial decomposition.

Each question carries 2 marks (double weightage), making this 5-question section worth a massive 10 out of 40 marks.

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4 Classic HOTS Archetypes in Class 3 IMO

Archetype 1: Fruit Balance Scale Substitution

The Problem:

Scale 1: 3 Apples = 1 Pineapple

Scale 2: 2 Pineapples = 1 Watermelon

Question: How many Apples balance 1 Watermelon?

How to Solve Visually: Instead of setting up equations, teach your child the "replacement game": 1. The watermelon wants to balance with pineapples first: it needs 2 pineapples. 2. Each pineapple can transform into 3 apples. 3. Therefore, 2 pineapples = $3 \text{ apples} + 3 \text{ apples} = 6 \text{ apples}$. 4. Answer: 6 Apples.

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Archetype 2: Cryptarithmetic Column Addition

The Problem: In the addition: 5 A 8 + 2 6 B = 8 4 1, find the value of A + B.

How to Solve with Column Deductions: 1. Look at the Ones column: $8 + B$ must end in a $1$. The only single digit is $B = 3$ because $8 + 3 = 11$. 2. This creates a carry-over of 1 into the Tens column. 3. Tens column: $1 \text{ (carry)} + A + 6 = 14$ (since hundreds column $1 + 5 + 2 = 8$). 4. $A + 7 = 14 \implies A = 7$. 5. Final calculation: $A + B = 7 + 3 = \mathbf{10}$.

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Archetype 3: Overlapping Sets (Venn Logic)

The Problem: In a class of 35 children, 22 like chocolate ice-cream, 18 like vanilla ice-cream, and 9 like both flavours. How many children do not like either flavour?

How to Solve: 1. Students liking at least one flavour = $(\text{Chocolate} + \text{Vanilla}) - \text{Both}$ 2. $= 22 + 18 - 9 = 40 - 9 = 31 \text{ students}$. 3. Students liking neither = $\text{Total} - 31 = 35 - 31 = \mathbf{4 \text{ children}}$.