Rearranging The Class Schedule
Logic
Level
2
Mark has signed up for 10 subjects. Every weekday, 2 of the 10 subjects are taught. When the semester ended, Mark was issued a new timetable for the next semester. Mark noticed that all of the changes were:
- Geography was on Thursday and now it is on Wednesday.
- Chemistry was on Thursday and now it is on Tuesday.
- Biology was on Friday and now it is on Thursday.
- History was on Tuesday and now it is on Friday.
- Physics was on Wednesday and now it is on Tuesday.
- Math was on and now it is on .
On which day did Mark use to have math class?
Tuesday
Thursday
Not enough information
Friday
Wednesday
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We can count a class that was on day x and now is on day y as -1 (one class less) on x day and +1 (one class more) on y day. Then we have:
From that we see that on Wednesday and Friday he would have the same number of classes than before (because one class would fill the gap let by the other) but on Tuesday he would have +1, which means that he was going to have 1 class more than the expected and on Thursday he would have 1 class less.
Since we know number of classes is equal every day the only solution to it, is that a class that was on Tuesday is now on Thursday, and that class can only be Math.
Note: the question ask when did Mark used to have math, not after the change.