The weather during Smedley's vacation was strange
-- It was cloudy on 13 different days but it was never cloudy for an entire day
-- Cloudy mornings were followed by clear afternoons
-- Cloudy afternoons were proceded by clear mornings
---There were 11 clear mornings and 12 clear afternoons in all
How long was the vacation?
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To determine the length of Smedley's vacation, we need to analyze the given information. Let's break it down step by step:
1. It was cloudy on 13 different days but never cloudy for an entire day: This means that there were some days with both cloudy mornings and clear afternoons.
2. Cloudy mornings were followed by clear afternoons: This means that there were no consecutive cloudy mornings and afternoons.
3. Cloudy afternoons were preceded by clear mornings: This means that there were no consecutive clear mornings and cloudy afternoons.
4. There were 11 clear mornings and 12 clear afternoons in total.
Based on this information, we can conclude that there must have been at least one day with a cloudy morning and a clear afternoon. Since there were 13 different days with cloudy weather, and none of them were completely cloudy all day, we can deduce that the vacation lasted for at least 13 days.
Additionally, since there were 11 clear mornings and 12 clear afternoons, it means that there is a single day where both the morning and afternoon were clear. This implies that there were at least 12 days in total.
Therefore, we can conclude that Smedley's vacation must have lasted for at least 13 days and at most 13 + 12 = 25 days.