By Guy Jacobson

This puzzle is titled “Great Tits!” because it is based on the Tits group, a finite group named for French mathematician Jacques Tits. (Also, the two birds shown are great tits, an Old-World passerine bird.)

The big block of text constitutes a presentation of the Tits group as a permutation group on 1600 elements (the characters of the text). The two birds represent two generators of this group, and clicking on either one applies the generator permutation to the text. So what we have here is essentially a transposition cipher, where the key is the member of the Tits group used to permute the plaintext to produce the ciphertext.

The Tits group is large, but not intractably so—it has about 18 million elements. On the assumption that the plaintext is English, a brute force enumeration of all the encodings followed by a check to see if the result looks like plausible English can be programmed up. This is a non-trivial programming task because you have to be somewhat careful about memory usage and efficiency. Here are some example implementations:

The block of text decrypts to what is mostly a sequence of very large numbers written out in English (broken into lines for readability):

ORDER GROUPS BY ORDER

FIRST NUMBER EIGHT HUNDRED EIGHT SEXDECILLION SEVENTEEN QUINDECILLION FOUR HUNDRED TWENTY FOUR QUATTUORDECILLION SEVEN HUNDRED NINETY FOUR TREDECILLION FIVE HUNDRED TWELVE DUODECILLION EIGHT HUNDRED SEVENTY FIVE UNDECILLION EIGHT HUNDRED EIGHTY SIX DECILLION FOUR HUNDRED FIFTY NINE NONILLION NINE HUNDRED FOUR OCTILLION NINE HUNDRED SIXTY ONE SEPTILLION SEVEN HUNDRED TEN SEXTILLION SEVEN HUNDRED FIFTY SEVEN QUINTILLION FIVE QUADRILLION SEVEN HUNDRED FIFTY FOUR TRILLION THREE HUNDRED SIXTY EIGHT BILLION

SECOND NUMBER SEVEN THOUSAND NINE HUNDRED TWENTY

THIRD NUMBER FIFTY ONE QUADRILLION SEVEN HUNDRED SIXTY FIVE TRILLION ONE HUNDRED SEVENTY NINE BILLION FOUR MILLION

FOURTH NUMBER NINETY QUADRILLION SEVEN HUNDRED FORTY FIVE TRILLION NINE HUNDRED FORTY THREE BILLION EIGHT HUNDRED EIGHTY SEVEN MILLION EIGHT HUNDRED SEVENTY TWO THOUSAND

FIFTH NUMBER SEVEN THOUSAND NINE HUNDRED TWENTY

SIXTH NUMBER FOUR QUINTILLION ONE HUNDRED FIFTY SEVEN QUADRILLION SEVEN HUNDRED SEVENTY SIX TRILLION EIGHT HUNDRED SIX BILLION FIVE HUNDRED FORTY THREE MILLION THREE HUNDRED SIXTY THOUSAND

SEVENTH NUMBER SEVEN THOUSAND NINE HUNDRED TWENTY

EIGHTH NUMBER FOUR BILLION THIRTY MILLION THREE HUNDRED EIGHTY SEVEN THOUSAND TWO HUNDRED

NINTH NUMBER FOUR HUNDRED NINETY FIVE BILLION SEVEN HUNDRED SIXTY SIX MILLION SIX HUNDRED FIFTY SIX THOUSAND

TENTH NUMBER TWO HUNDRED SEVENTY THREE TRILLION THIRTY BILLION NINE HUNDRED TWELVE MILLION

ELEVENTH NUMBER SEVEN THOUSAND NINE HUNDRED TWENTY

TWELFTH NUMBER ONE HUNDRED FORTY FIVE BILLION NINE HUNDRED TWENTY SIX MILLION ONE HUNDRED FORTY FOUR THOUSAND

These twelve numbers are all orders of Sporadic groups. (Google searching any of the larger numbers will reveal that fact.) Note that the Tits group is sometimes regarded as an honorary member of the sporadic groups. There are exactly twenty-six sporadic groups, and the instruction “ORDER GROUPS BY ORDER” tells solvers that the groups should be ordered from the smallest (lowest order) to the largest. Since there are twenty-six groups, each one can map to a letter of the alphabet, with the smallest group (the Matthieu Group M11) corresponding to A and the largest group (the monster group M) corresponding to Z.

Using this mapping, the sequence of twelve order numbers translates to ZASTAVA KORAL, the solution to this puzzle. This is the official make and model of the car usually called the Yugo (confirmed by the “You go . . . ” that begins the flavortext).