11 of 100: 999 Sentences

Logic Level 3

Suppose the alternating pattern below continues for 998 sentences before ending with one unique sentence.

1) The next sentence is \(\color{blue}\text{true}\color{black}.\)

2) The next sentence is \(\color{red}\text{false}\color{black}.\)

3) The next sentence is \(\color{blue}\text{true}\color{black}.\)

4) The next sentence is \(\color{red}\text{false}\color{black}.\)
...
997) The next sentence is \(\color{blue}\text{true}\color{black}.\)

998) The next sentence is \(\color{red}\text{false}\color{black}.\)

999) \(Y\geq5\)

I'm thinking of a number, \(Y.\) If sentence 1 is true, what do you know about \(Y\)?

Be systematic! In our opinion, this is the hardest problem so far, especially if you play around with generalizing it to more complex patterns of "The next sentence is \(\color{blue}\text{true}\color{black}/ \color{red}\text{false}\color{black}\)" than the alternating pattern above. We hope you enjoy it! :)

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