Extraterrestrial integer value representation

exercise No. 218


A group of scientists captured an extraterrestrial radio signal. While deciphering its content the group concludes the three subsequently provided words represent three different integer values:

xzqllxv vlf yppa

The alien civilization uses {x,z,q,...} rather than {0,1,2,3,4,5,6,7,8,9} for representing digits. The scientists assume »regular« numbering behaviour like e.g. being used in position based number representations you've learned about in your lectures.

The radio signal is limited: The scientists thus neither know the individual digits' values nor their overall count.

For practical reasons we typically use base 2 (binary), base 8 (octal), base 10 (decimal) or base 16 (hexadecimal) number representing schemes. From a fundamental point of view however every base value starting from 2 onwards might be chosen.

Which number base values of the underlying representation can be ruled out by the above three integer sample values? Could it for example be binary? Explain your answer.


The yet unknown numbering scheme uses at least 9 digits:


The integer representing system's base must thus be 9 or larger ruling out base values ranging from 2 (binary) to 8 (octal).