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Here's a solution from a group of eighth graders at Monroe City Middle School in Monroe City, MO:

Our names are Allie, Erica, Micah, Kimberly, and Tina. We found this problem fairly simple. This is how we found the answer:

The first clue said that the upside down v equals 1. The butterfly and the upside down v equaled 5. Then it said that if the symbols were side by side, then it meant plus so the butterfly and the upside down v had to equal 5 so the butterfly equaled 4.

The next clue said that 2 upside down v's equaled an upside down triangle; that would equal 2. The 2 butterflies equaled 8 so the filled in square equaled 8. So the hourglass minus the upside down triangle(2) equaled the upside down triangle plus the filled-in square plus the butterfly(14). That meant the hourglass equaled 16.

With the given numbers, the shortest way to write 21 was the hourglass plus the upside down v plus the butterfly.

teacher: Mrs. Barbara Carson

eeps replies:

Thank you for sending in your solution! Here's something to think about: different groups come up with different names for the symbols. For example, you used "butterfly," others use "bow tie." How does that affect how well you can communicate? Do you ever see anything else in life where people use different names for the same thing and get confused?

Dear Mr. Erickson,

We are fifth grade students from Maplewood school in Cary, Illionis. We think we found out the answer to your znorlian question. We made twenty-one with three symbols. The hour glass equals sixteen, the bow tie equals four, and the tipee equals one. We hope the answer is right.

Christina Claveria
Nicole Schroeter
Fedrick Burgos
Dan Schwan Mary McGuire Cary School District#26

eeps replies:

Thank you for sending in your solution! I'd love to see more from you, especially if you include HOW you got your answer. Meanwhile, see how you gave different names to the symbols than the group from Monroe City, above? Did you get the same answer they did?

We thought there was nothing new to say about this problem, but then the assiduous students of Hermann, MO sent this (March 2008):

We are Mrs. Dann's 7th grade enrichment class from Hermann Middle School in Hermann, MO. We have solved the Znorlian quandary. Along with the students from Monroe City and Cary, we discovered that the hourglass, bowtie, and caret symbols combine to create the number 21 in the Znorlian number system.

We also found that the Znorlian number system highly resembles the binary code. One way the two are similar is that they both have a base of two. The caret is a 1; the triangle is 2; the bowtie is 4; the rectangle is 8; and the hourglass is equal to 16. This is like the binary system in that when you increase a place value you multiply the base by 2. So the places in binary are 1, 2, 4, 8, and 16

There are some differences though. The binary code only uses 1s and 0s. Znorlian has at least 5 symbols. The binary code however uses place value but Znorlian uses addition of the symbols to get a new number.

Interesting observation! Two things I especially like about this (besides how interesting the observation is) are:

  • You referred to the work that other students had done.
  • You used semicolons really, really well :)

Keep up the good work!

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