Sandy Wood
Brain Game: The Monthlies
by Sandy Wood - August 13, 2009 - 7:30 AM

bloghead_braingames.jpg

It may take you days to solve today’s Brain Game. In fact, I guarantee that it will, because it’s about calendars. Suppose you’re a craftsman that likes to print calendars using wooden blocks. You’ve designed a grid exactly like this one:

calendarNow, it’s time for you to carve the wood blocks that will represent the dates. You want to create one printing block for each possible space on the calendar, including blanks. Considering how calendars vary from month-to-month and year-to-year…

How many different blocks would you have to carve
to fit inside the above grid to handle ALL possible months?

Here is the SOLUTION.
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Comments (17)

  1. Wouldn’t it be only 33, since for the blank squares you could just turn one of the carved blocks on its side?

    posted by Garrett on 8-13-2009 at 8:49 am

  2. But you would be using those blocks, so you couldn’t turn them all on their side. Only the left over ones for each month. I think you would need at least 5 blank blocks.

    posted by Bill on 8-13-2009 at 9:04 am

  3. Oh you’re right… but either way I think the answer would still be less than what was posted.

    posted by Garrett on 8-13-2009 at 9:06 am

  4. If the “23″, “24″, “30″ and “31″ blocks were used on the reverse side for blanks, the could be used in Feb and when the 1st falls on a Saturday. The split date blocks could be used in the same fashion meaning you would only need 3 blanks dropping your number needed by 4.

    posted by KevinGA on 8-13-2009 at 9:32 am

  5. Remember the rules, though, folks: We’re asking for “one printing block for each possible space on the calendar, including blanks.”

    This would preclude the use of the other sides of blocks as blanks, and also means that no block could have numbers on more than one side.

    posted by Sandy Wood on 8-13-2009 at 10:16 am

  6. I got 44
    you need 11 blanks, example May 09

    posted by Lee on 8-13-2009 at 11:17 am

  7. @Lee – Check out the grid again. You would not have the 31st fall on its own week.

    As an interesting note, I did the puzzle incorrectly. However, I did discover that if you want a single block to print the entire month, you only need 28 blocks. February needs 14 (seven for regular years, seven for leap years), the 31-day months need 7, and the 30-day months need 7.

    posted by Lugh on 8-13-2009 at 11:36 am

  8. I was two off. (darn splits)

    Lee, May ’09 takes that many blocks if you had an area of 7×6. Sandy gave us a 7×5 to work with.

    Lets also pretend that these blocks aren’t necessarily perfect cubes either (only one face can be used), so the printing on all sides wouldn’t work.

    posted by Steven on 8-13-2009 at 12:27 pm

  9. I found an example. as you can see by this LEGO timetable the blocks cant exactly be flipped around and used on any other side for any other purpose.

    posted by Steven on 8-13-2009 at 12:40 pm

  10. I stand corrected

    posted by Lee on 8-13-2009 at 12:45 pm

  11. Wouldn’t you just need 35, one for each square?

    so the breakdown would be:
    1 – 31 and 4 blanks.
    23 and 24 could have the split dates on the reverse side.
    29 thru 31 would be blank on the reverse

    posted by joe on 8-13-2009 at 2:34 pm

  12. We accept those split date blocks because we’ve been taught to. There is nothing that requires that form. Put the 30 and 31 blocks in the blanks at the top (and teach the user to accept that as the end of the current month). You’d then need 7 blanks plus 31 dates –> 38 blocks.

    posted by loomis on 8-13-2009 at 3:10 pm

  13. @loomis

    that was my first idea, we have that convention on calendars in australia all the time. in fact i thought it was strange to see the split date idea.

    posted by johnson on 8-13-2009 at 6:51 pm

  14. If you want to get REALLY technical, those “blank” slots could just be the dates of the previous and next months. With that said, it would move the total to 47 blocks.

    The previous month would have to go as far back as 23 to make up for February (non-leap year) and the 28th would fall on a Friday on Sandy’s calendar above where the current month’s 1st day would fall on a Saturday. On the other end, it could start at 1, and work its way up to 7 because a non-leap year February would only fill four of the five rows.

    So, the 9 blocks needed to fill the previous month, the 7 needed for the next month (given you start the first block with the 1st of the current month), and the 31 needed for the current month, the total comes to 47 blocks needed.

    posted by Steven on 8-13-2009 at 11:02 pm

  15. oops, i forgot split dates again, haha.

    49! 49 blocks!

    posted by Steven on 8-13-2009 at 11:04 pm

  16. wow! I was just excited that this is the first brain game in weeks I got all by myself…

    posted by Michele on 8-13-2009 at 11:20 pm

  17. 28

    posted by anonymous on 8-18-2009 at 4:54 pm

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