The days of the week repeat every 7 days — that one fact answers almost every calendar question. And when a question asks "in how many ways", it is really just asking you to count carefully.
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There are only 7 days of the week, and they repeat forever. If you go forward exactly 7 days, you land on the same day again.
Mon → Tue → Wed → Thu → Fri → Sat → Sun → Mon …
To find the day after a number of days, divide that number by 7 and look at the remainder only.
Shortcut: if the remainder is 0, the day is the same as the day you started on — no counting needed!
Not every month has the same number of days — and February gets one extra day in a leap year.
31 days
Jan, Mar, May, Jul, Aug, Oct, Dec
30 days
Apr, Jun, Sep, Nov
28 or 29 days
February only
🔑 The leap year rule
A year is a leap year if it can be divided evenly by 4 — then February gets 29 days instead of 28.
(A very few century years like 1900 break this rule, but you will not need that exception at this level.)
"In how many ways" questions want you to count every possible choice, without missing any and without repeating any.
The multiplying rule: if one choice can be made in a ways and a second, separate choice can be made in b ways, the two together can be made in a × b ways.
12 IMO-style questions on days, dates and combinations. 🍀
