Lorith
(page 32)

Here is a solution from 2008, from "the S.T.A.R.S. from Hermann Middle School." Note their explanation. Does their method give different results from the other groups? Is there any advantage of one method over the other?

We have solved the Lorith number system and completed the multiplication  table. Both of the other groups that have solved this problem first multiplied in our number system, and then translated the answer  that they got into Lorith. For example, for 4x4, they both did it in our number system. They did 4x4=16. 16 is 220 in Lorith.  However, we multiplied 10x10, 11x11, 20x20, 21x21, etc. But we made sure that our place values were correct.  We found that  the last place value can only be 1 or 0. The second to last place value can only be 0, 1, or 2. The third place value could only go up  to 3. The fourth can go up to 4, etc. First, we found out how someone would go about adding in Lorith. Then, we started making out  multiplication table. 

  1 10 11 20 21 100 101 110
1 1 10 11 20 21 100 101 110
10 10 100 110 200 210 1000 1010 1100
11 11 110 121 220 301 1100 1111 1210
20 20 200 220 1000 1020 2000 2020 2200
21 21 210 301 1020 1111 2100 2121  
100 100 1000 1100 2000 2100 10000 10100 11000
101 101 1010 1111 2020 2121 10100 10201 11110
110 110 1100 1210 2200 2310 11000 11110 12100

And now, the first solution of 2005, from Daniel, Danny, and Chris—6th graders from the Progressive School of Long Island in Merrick, New York.

In Lorith, the last place value is one, according to one of the clues. The second to last digit is the two’s place. The third to last digit is the six’s place, and the fourth to last is the twenty-four’s place. There is a pattern to figuring out these places, and that is to add one to the second factor and then multiply by the previous product (after the first term), such as 1x2=2, 2x3=6, 6x4=24, etc. According to this theory, that would make our 3 Lorith’s 11, and our 4 Lorith’s 20.

         ____ ____ ____ ____
          24    6    2    1
Here is what our chart looks like. It would translate to our multiplication table from 1 through 8.
| 1 10 11 20 21 100 101 110 -----+--------------------------------------- 1 | 1 10 11 20 21 100 101 110 10 | 10 20 100 110 120 200 210 220 11 | 11 100 111 200 211 300 311 1000 20 | 20 110 200 220 310 1000 1020 1110 21 | 21 120 211 310 1001 1100 1121 1220 100 | 100 200 300 1000 1100 1200 1300 2000 101 | 101 210 311 1020 1121 1300 2001 2110 110 | 110 220 1000 1110 1220 2000 2110 2220

At last a solution to Lorith from the planet B-612. But where is their embassy on Earth?

This is Ben Ahrens, Nag Young Kwak, and Gun Woo Kim's solution to the Lorith alien number system on page 32 in the United We Solve book. This was easy for us because on our planet we use this system. We are from the planet B-612.

      1     2     3     4      5      6     7     8
1   001   010   011   020    021    100   101   110

2   010   020   100   110    120    200   210   220

3   011   100   111   200    211    300   311  1000

4   020   110   200   220    310   1000  1020  1110

5   021   120   211   310   1001   1100  1121  1220

6   100   200   300  1000   1100   1200  1300  2000

7   101   210   310  1020   1121   1300  2001  2110

8   110   220  1000  1110   1220   2000  2110  2220

eeps says:

Thank you for your solutions! I leave it to readers to decide if they are right. Then there's the issue of describing how you know that you've understood the number system correctly. What do you think of these solutions' explanations of the number system? If a group is confused, do they help you understand what's going on?

And here's something to ponder: if you have learned about properties of number systems, how different is Lorith's from our own? For example, what operations commute? Are there still identity elements? What is the story on place value in Lorith? And what do you think their hands look like...:)

--eeps

You know, you can answer these questions too! Just write to !

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