Way back in 1961, a conference was held in the United States on the possibility of intelligent extraterrestrial life, in fact the first SETI (Search for Extraterrestrial Intelligence) conference. After the meeting, the radio astronomer Frank Drake set the delegates a puzzle to solve. Imagine, he suggested, that a radio message is received consisting of 551 characters of just two different kinds, like a series of 0's and 1's or A's and B's. He specified the values of the 551 characters received, and that was the only clue he provided for solving the puzzle!
The mathematically minded would realise that 551 has just two prime factors, 19 and 29. This suggests something 2-dimensional, a picture perhaps.
There are two fundamentally different possible pictures in that case, 19 characters wide and 29 high, or vice versa. 29 characters wide and 19 high gives us the result to the left below, which is not very promising. Vice versa to the right, and that is certainly more suggestive!
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Apart from the most obvious thing, what else might we recognise in the picture? I'll provide some clues.
1. There is a large square at the top left, and below that the third square from the left is always white, so that there is a white stripe from top to bottom.
2. To the left of that stripe, going down from the large square, there are four single squares, a double one, two quadruple ones, another double, and a final single. If we think of those as four small, a medium, two large, another medium and another single, isn't that reminiscent of something familiar - especially adding in the very large one at the top left?
3. Sorry to be mathematical again, but recall binary numbers such as computers use. Apparently in computing it is useful if every binary number has an odd number of 1's, to distinguish it from things that are not meant to be numbers. So a binary number like 110 (6, of course, in decimal) has a "parity bit" added, making it 1101. Then there are three 1's instead of just two. Of course it is necessary to distinguish the parity bit from the actual number in some way. Don't ask me how that is done in computer language, because I don't know! But looking to the right of the white stripe, what can we see? And notice that there is another white stripe right from the top of the picture to - well, what can it be but part of the alien's head? And to the right of that stripe, what have we got?
4. Even more mathematical, 232 is about 4 billion. 210 is 1,024.
5. A bit of chemistry now - a carbon atom has two electrons in its inner shell, and four in its outer shell. An oxygen atom also has two electrons in its inner shell, and six in its outer.
6. The aliens and us would have a unit of length in common - the wavelength of the radio signal they sent!
What can you work out from those clues?