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### The Solution

The reference for this problem and its solution is Martin Gardner, Martin Gardner's Sixth Book of Mathematical Games from Scientific American, chapter 25. The following solution is quoted from Gardner.

1. [This simply states the 24 symbols.]
2. [This identifies the first 10 symbols (A through J) with the numbers 1 through 10.]
3. [Symbols for ``plus'' and ``equals'' are introduced.] 1+1=2; 1+1+1=3; 1+1+1+1=4. 1+1=2; 2+1=3; 3+1=4; 4+1=5. 2+5=7; 7=5+2. 6+4=10; 10=6+4.
4. [The minus sign is introduced.] 3-1=2; 4-1=3; 9-7=2.
5. [Zero is introduced.] 3+0=3; 8+0=8. 4-4=0; 5-5=0.
6. [Positional notation, based on 10, is introduced. J=AN translates J into the decimal form 10.] 10+1=11; 10+2=12; 11+1=12. 10+10=20; 10+10+10=30. 60+7=67.
7. [The multiplication symbol is introduced.] ; ; .
8. [The division symbol is introduced.] ; ; .
9. [Exponents are introduced.] ; .
10. [Symbols for 100 and 1,000 are introduced.] ; . ; .
11. [Symbols for 1/10 and 1/100 are introduced.] ; .
12. [The decimal sign is introduced.] 1/10=.1; ; . 1/100=.01; . ; . ; .
13. [The sign for ``approximately equal to'' is introduced.] ; . [The sign for is introduced.] .
14. .
``The final statement is the formula for the volume of a sphere with a radius of .0092. As Bell recognized when he gave the answer to his message (Japan Times, January 29, 1960), there is an ambiguity here that could have been avoided only if information about the use of brackets or the order in which arithmetic operations are to be performed had been given previously. The formula suggests that an actual sphere is being described. If the receivers of the message are on a planet in our solar system, they should be clever enough to deduce that the sun's radius is providing the unit of length, and that the radius of the third planet from the sun is .0092 of the sun's radius. The expression therefore gives the volume of the earth and is a sign-off statement indicating the source of the message.''

Next: Properties of Natural Numbers Up: Using Arithmetic for Extraterrestrial Previous: The Message

Carl Lee
Wed Sep 16 09:26:16 EDT 1998