We have ten fingers. This is probably why we count in base ten. Octopuses have eight tentacles.
Let’s imagine that they count like us but on their eight tentacles. This gives 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, etc. Thus 123 into account octopus means 82 + 2.8 + 3 for us, or 83 in base ten.
What are then the quotient and the remainder of the division of 7654321 by 1234567 in octopuses?
Answer
6 and 7. Of course, we can translate these two numbers A = 7654321 and B = 1234567 in base ten but it’s long and not very pretty (we find 2054353 and 342391 which are easy to divide). It is easier to calculate as one of these mythical octopuses would. By adding A and B, we notice that A + B = 11111110 and, similarly, 8A = 76543210 therefore 8A + B = 77777777 therefore 8A + B = 7 (A + B + 1) hence A = 6B +7, which means that the quotient of A by B is 6 and the remainder is 7.
Learn more about Hervé Lehning
Ecole Normale Normale and maths graduate, Hervé Lehning taught his discipline for a good forty years. Mad about cryptography, member of the Association of encryption and information security reservists, he has in particular pierced the secrets of Henri II’s cipher box.
Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.
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