Pulling on Plastic
Probability
Level
2
I climb for 10 hours every week. If I climb for the same amount of time every time I go to the gym, climb for a whole number of hours, avoid going 3 consecutive days, and always climb on Tuesdays and Thursdays, how many combinations are there of days I can climb?
21
2
1
5
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1 solution
While this problem can be solved with combinatorics (and probably should), there's an easier solution: If I climb 10 hours per week, and climb for the same amount of time every time, there are 4 ways to do so: 1 hour 10 days per week, 2 hours 5 days per week, 5 hours 2 days per week, or 10 hours 1 day per week. However, there aren't 10 days in a week (unless I'm missing something), so I can't climb 1 hour per day. Also, I have to climb on 2 specific days, so I can't climb for 10 hours on 1 day. That leaves only two options: 2 hours on 5 days of the week or 5 hours on 2 days. Both would appear to be viable answers, but I don't want to climb three or more days in a row. (Increased risk of injury, and injuries aren't fun.) There's no way to pick 5 days of the week without picking 3 or more consecutively, leaving one possible combination.