A Real-Life Puzzle
This is a real-life puzzle which I thought you might enjoy trying to solve.
I am a first and second grade teacher and, like many primary teachers, I do a calendar activity with my students
in which we start each month with a blank calendar and add a new date card to the calendar each day. The card has
on it the number for the day's date and something about it that creates a sequenced pattern--e.g., a picture, a
color, a position of the number, etc. As the month progresses the students try to figure out what the pattern is
and then predict each day what that day's card will look like before we put it up. I also make the cards
coordinate with the unit we are studying that particular month.
This puzzle started in January, a brand new month in a brand new year! Our class was going to study rocks and
minerals, so I had gotten out my resource box on rocks and was happy to find my calendar cards for the unit right
where they were supposed to be, right there where I had put them the last time I had done this unit two years
previously. On January 4th, the first day back to school from Winter Break, I blithely began our calendar time
by putting up the first card. It was a card with a black numeral one in the middle and a white pebble glued at
the center of the bottom side. The students made various predictions for the next card: a different colored
pebble, two pebbles instead of one, a different colored numeral, etc. I put up the second card. It was a card
with a black numeral two in the middle and a white pebble glued at the center of the right side. The students
again made predictions and I put up the third and fourth cards. We did the same the next two days. The pattern
wasn't obvious to me at this point, but I wasn't really concerned since I knew that sometimes in the past I had
made patterns that took six or seven or eight days to repeat.
As it turned out, the next two days were snow days, the next two were the weekend, and the next day I was away
from my class for a science in-service and had a substitute. When we were ready to do our calendar time on the
12th, I looked at the calendar and realized that I had no earthly idea what that pattern was supposed to be!
I admitted it to my students and told them I would sit down after school and try to figure out what was going
on. This is what our calendar looked like at that point.
CAN YOU FIGURE OUT WHAT WAS GOING ON? (Please remember that this was a pattern which I had successfully used with
1st and 2nd graders a previous year. You can also eliminate the possibility that some of the pebbles had come
unglued and had then been glued back in the wrong place--I checked for that.)
If you figured out the solution based on that much information, you are a better problem solver than I am. I
ended up getting out the cards for the rest of the month (shown below). I finally had that satisfying "Ah-ha"
feeling of solving the mystery, but it wasn't immediately obvious. CAN YOU DO IT?
Published in Lexington Council of Teachers of Mathematics Newsletter, February/March, 1999.