D. Base‑16 (hexadecimal) curiosities Does there exist a hexadecimal number that,

D. Base‑16 (hexadecimal) curiosities

Does there exist a hexadecimal number that, when multiplied by 2, 3, 4, 5, and 6, yields numbers that are permutations of its digits (in base 16)?

Find a hexadecimal number that increases by an integer factor when its last digit is moved to the front (both operations understood in base 16).

E. Last digits and modular arithmetic

Determine the last digit of 3377 + 7733.

Find the last two digits of 22000.

What is the last digit of 9,999,999,999?

Find the last digit of 9999(99999999).

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