Library / UKMT Senior Kangaroo /96 of 139

UKMT Senior Kangaroo, 2024

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The seventh day of an unknown month in an unknown year is a Tuesday. The $n$ th day of the following month is the first Tuesday of that month. What is the product of all the possible values of $n$ ?

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.