Content-Type: text/shitpost


Subject: Testing for divisibility by 99
Path: you​!your-host​!walldrug​!epicac​!goatrectum​!plovergw​!shitpost​!mjd
Date: 2017-12-13T23:50:37
Newsgroup: comp.protocols.tcp-ip.math.multiple-of
Message-ID: <54a2906b663f862c@shitpost.plover.com>
Content-Type: text/shitpost

Mathematically this is a nothing, but it's fun and I hadn't seen it before. Pick a number, say 852143, and multiply it by 99, giving $$84362157.$$

Now break this up into two-digit chunks:

$$84\qquad 36\qquad 21\qquad 57$$

(If there is an odd number of digits, put the leftmost one in a chunk by itself.)

Add up the chunks:

$$84 + 36 + 21 + 57 = 198$$

Repeat the process:

$$1 + 98 = 99$$

You will always finish at 99.

This same method can be used to test a number to see if it is divisible by 99: you can start with any number you like, and you will end at 99 if and only if the number you started with is a multiple of 99. (If the starting and ending numbers are !!s!! and !!e!!, then !!s\equiv e\pmod{99}!!.)

The trick is, of course, completely analogous to the test for divisibility by 9. Maybe you know some mathematical kid who has recently learned the divisibility-by-9 test and would enjoy seeing this version.