Two-step Think of a Number Puzzles

These are a collection of mathematical puzzles designed to challenge one's problem-solving skills. Each puzzle starts with an instruction to think of a number, followed by a sequence of mathematical operations - multiplication and either addition or subtraction. The final result of these operations is provided, and the objective is to work backwards to deduce the original number thought of. For example, if you multiply a number by 3 and add 1 to get a result of 10, you need to reverse the operations to find the starting number. Similarly, in another puzzle, if you multiply a number by 2, add 2, and the final answer is 10, you would work out what the original number was using the given outcome.

The puzzles vary in complexity, with different multipliers and different numbers to add or subtract. For instance, one puzzle might involve multiplying the original number by 4 and adding 1 to arrive at a final answer of 33, whilst another could require multiplying by 5 and adding 2 to reach a result of 47. Other puzzles involve subtracting a number after multiplication, such as multiplying by 7 and subtracting 1 to get an answer of 48. Each puzzle is a fun and engaging way to apply basic arithmetic operations and test one's ability to think algebraically. The goal is to understand the relationship between the operations performed and the final result to uncover the starting number.