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Home » 2r - (3 - \sqrt5)r + 5 - \sqrt5 = 0 - AMAZONAWS

2r - (3 - \sqrt5)r + 5 - \sqrt5 = 0 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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We proceed as follows for one fixed $ i $:
Choose the repeated digit: 3 choices.
For the digit at position $ i-1 $ (if it exists), it must be different...
For the digit at position $ i+2 $ (if it exists), it must be different...
All other digits must alternate and differ from their neighbors.
Letâs compute the number of such sequences for each position:
#### Case: Repeated pair at (1,2)
$ d_1 = d_2 $: 3 choices
$ d_3
eq d_2 $: 2 choices

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