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Omni-MATH / Mark and William are playing a game with a stored value. On his turn, a player…

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problem

Mark and William are playing a game with a stored value. On his turn, a player may either multiply the stored value by 2 and add 1 or he may multiply the stored value by 4 and add 3. The first player to make the stored value exceed 21002^{100} wins. The stored value starts at 1 and Mark goes first. Assuming both players play optimally, what is the maximum number of times that William can make a move?
Plain-text mathematical notation (without MathML)
Mark and William are playing a game with a stored value. On his turn, a player may either multiply the stored value by 2 and add 1 or he may multiply the stored value by 4 and add 3. The first player to make the stored value exceed 2¹⁰⁰ wins. The stored value starts at 1 and Mark goes first. Assuming both players play optimally, what is the maximum number of times that William can make a move?
Original LaTeX notation
Mark and William are playing a game with a stored value. On his turn, a player may either multiply the stored value by 2 and add 1 or he may multiply the stored value by 4 and add 3. The first player to make the stored value exceed $2^{100}$ wins. The stored value starts at 1 and Mark goes first. Assuming both players play optimally, what is the maximum number of times that William can make a move?

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Source and history

task_id
c5229982-5d6f-542e-b5ea-5dbfcb3c0164
task_key
test--c5229982-5d6f-542e-b5ea-5dbfcb3c0164
task_revision_id
1
config / split
/ test

Official source

initial import