An easy question on number puzzles for P1–P2, with a step-by-step solution, diagrams and the answer. Number puzzles and made-up operations appear in the Hua Xia Cup from the P1 and P2 first rounds to the P6 finals.
The question
The teacher makes up a new operation, ◎.
The first line below is its rule; the second is an example.
a ◎ b = a × 2 + b2 ◎ 3 = 2 × 2 + 3 = 7
What is 5 ◎ 9?
Show the hints (2)
💡Hint 1: The number before ◎ goes where a is, and the number after it where b is — just like the example.
💡Hint 2: Put 5 in place of a and 9 in place of b, then follow the rule.
Worked solution
Have a go first, then read the solution step by step.
1.a is 5 and b is 9: 5 ◎ 9 = 5 × 2 + 9 = 19.
⚠️Common mistake: swapping the two numbers and working out 9 × 2 + 5 = 23.
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