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