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Omni-MATH / The number 770 is written on a blackboard. Melody repeatedly performs moves,…

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problem

The number 770 is written on a blackboard. Melody repeatedly performs moves, where a move consists of subtracting either 40 or 41 from the number on the board. She performs moves until the number is not positive, and then she stops. Let NN be the number of sequences of moves that Melody could perform. Suppose N=a⋅2bN=a \cdot 2^{b} where aa is an odd positive integer and bb is a nonnegative integer. Compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
The number 770 is written on a blackboard. Melody repeatedly performs moves, where a move consists of subtracting either 40 or 41 from the number on the board. She performs moves until the number is not positive, and then she stops. Let N be the number of sequences of moves that Melody could perform. Suppose N=a⋅2^(b) where a is an odd positive integer and b is a nonnegative integer. Compute 100a+b.
Original LaTeX notation
The number 770 is written on a blackboard. Melody repeatedly performs moves, where a move consists of subtracting either 40 or 41 from the number on the board. She performs moves until the number is not positive, and then she stops. Let $N$ be the number of sequences of moves that Melody could perform. Suppose $N=a \cdot 2^{b}$ where $a$ is an odd positive integer and $b$ is a nonnegative integer. Compute $100 a+b$.

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Source and history

task_id
321cc06f-322a-52c0-9ae5-655b7846df72
task_key
test--321cc06f-322a-52c0-9ae5-655b7846df72
task_revision_id
1
config / split
/ test

Official source

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