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There is great excitement in the astronomy community. The search for extraterrestrial intelligence is finally bearing fruit. A strong clear repeating signal is being received from a not so distant star. The pattern being transmitted is as follows.

A AB AACABB ABA AABCABBB AAACABBA ABAB AABBCABBBB

A represents a high pitch tone, B a low pitch tone, and C a tone that oscillates rapidly between the two.

The message lasts for roughly 14 seconds, then stops for about half an hour before repeating again. The time between each repetition is decreasing by about 35 seconds each time.

After the expected duration the message changes.

The original message is still present but when it ends a new message starts after a few second pause.

AAAAAAAAAAAAAAAAAAAAAABACADAAAAAAAAAAAAAAAAAAAAAAAAAAAABEACADDAAAAAAAAAAAAAAAAAAAAAAAAAABEEACADDDAAAAAAAAAAAAAAAAAAAAAAAAABEBACADDDDAAAAAAAAAAAAAAAAAAAAAAABEEEACADDDDDAAAAAAAAAAAAAAAAAAAAAABEEBACADDDDDDAAAAAAAAAAAAAAAAAAAAABEBEACADDDDDDDAAAAAAAAAAAAAAAAAAABEEEEACADDDDDDDD

This new message is much longer than the first and with different tones, each a a different frequency.

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  • $\begingroup$ I can't believe that another astronomy question was posted right before my own one! What a coincidence! $\endgroup$ – leoll2 May 16 '15 at 14:40
  • $\begingroup$ @Bob Some other puzzler has bugged your computer! ;-) $\endgroup$ – Rand al'Thor May 16 '15 at 14:46
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    $\begingroup$ Is it possible to solve this puzzle with no knowledge of music? $\endgroup$ – Rand al'Thor May 16 '15 at 15:50
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    $\begingroup$ What exactly is the message is not clear to me but it is someone that will hit earth (if the time stays exactly 35 seconds between messages it means that the move is directly to the earth) in about 30*60/35 repetitions. You may estimate the speed (the speed of light multiplied by 35). The message could be: "I can not stop (please?) move away" $\endgroup$ – Moti May 16 '15 at 18:20
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So the aliens are counting in binary. Here's the signal with A replaced with 1, B replaced with 0, and C replaced with ':'

1 10 11:100 101 110:1000 111:1001 1010 1100:10000

They're telling us they have three fingers! Here's a commentary:

One, two, three:ten, eleven, twelve:one hundred, thirteen:one hundred and one, one hundred and ten, one hundred and a hundred:thousand

Everytime they run out of fingers, they add C[base increment] to the number. This should be our response:

1 10 11 101 111 1000 1001 1010 1011 1100C10000

Hopefully that will be enough to let them know we understand their message, and we have ten fingers!

Edit: If they "count one, two, ten" then they have three fingers, not two.

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  • $\begingroup$ I don't understand how you converted the binary into a message. Also, what's the meaning of ":" ? $\endgroup$ – leoll2 May 18 '15 at 16:17
  • $\begingroup$ : is just what I replaced C with. I've replaced the characters A, B, and C with 0, 1, and ":". It's not a message, it's a pattern, it's showing that everytime they want to count three, they say ten. Everytime they want to count thirteen, they say one hundred, etc. $\endgroup$ – Mark May 18 '15 at 16:19
  • $\begingroup$ Hmmm, then we know that they know the meaning of three. We can speculate that they have 3 fingers when born, then amputee one for a some kind of ritual $\endgroup$ – leoll2 May 18 '15 at 16:23
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    $\begingroup$ We can't make that deduction, they know the meaning of three exactly as much as we know the meaning of eleven, they're just telling us what base their counting system is in $\endgroup$ – Mark May 18 '15 at 16:25
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    $\begingroup$ That said, they'd have no reason to skip 111 if they were actually counting in binary. Base 2 usage doesn't care what your "native" base is, any more than we'd skip 11, 12, 13, 14, and 15 when counting in hex. I suspect this answer is close, though. $\endgroup$ – Bobson May 18 '15 at 18:31

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