We Got A Problem #1: 6/5/11

Today is June 5, 2011, or 06-05-11 in shorthand (05-06-11 in many countries).

Interestingly, 06 + 05 = 11.  How many more times in this century will it happen that the month number plus the day number equal the last two digits of the year number?

We’d love for readers to be able to explore this problem, so resist the urge to provide answers in the comments.  Instead, we’d love helpful suggestions and ideas about different ways to approach the problem, successful or not.  If you’d like to provide a full solution, do so with a pingback to your own blog!


About Bowen Kerins
Bowen is a mathematics curriculum writer. He is a lead author of CME Project, a high school curriculum focused on mathematical habits of mind, and part of the author team of the Illustrative Mathematics curriculum series. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won $1,000 for knowing the number of degrees in a right angle.

2 Responses to We Got A Problem #1: 6/5/11

  1. jim says:

    I started with the constraints: What’s the largest number I can make by adding the month and day? What’s the next one, not counting 6/5/11? What’s the smallest?These gave me boundaries. Then I started just figuring them out for each year, looking for patterns and exceptions (no Feb 30, etc.). I ended up making a spreadsheet and counting them up there.

    The problem seemed a little daunting at first but once I started defining the edges and filling in some pieces, it wasn’t bad. Like a jigsaw puzzle.

  2. sebbamath says:

    I found a few patterns but there was a lot of brute force involved.


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