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Omni-MATH / Abbot writes the letter A on the board. Every minute, he replaces every occurrence of A with AB and every occurrence of B with BA, hence creating a string that is twice as long. Af…

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problem

Abbot writes the letter AA on the board. Every minute, he replaces every occurrence of AA with ABA B and every occurrence of BB with BAB A, hence creating a string that is twice as long. After 10 minutes, there are 210=10242^{10}=1024 letters on the board. How many adjacent pairs are the same letter?
Plain-text mathematical notation (without MathML)
Abbot writes the letter A on the board. Every minute, he replaces every occurrence of A with AB and every occurrence of B with BA, hence creating a string that is twice as long. After 10 minutes, there are 2¹⁰=1024 letters on the board. How many adjacent pairs are the same letter?
Original LaTeX notation
Abbot writes the letter $A$ on the board. Every minute, he replaces every occurrence of $A$ with $A B$ and every occurrence of $B$ with $B A$, hence creating a string that is twice as long. After 10 minutes, there are $2^{10}=1024$ letters on the board. How many adjacent pairs are the same letter?

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task_id
0252ed2c-7539-5c66-b4ee-ff43ee1f27a8
task_key
test--0252ed2c-7539-5c66-b4ee-ff43ee1f27a8
task_revision_id
1
config / split
/ test

Official source

initial import