Numbers, Reverses, and Sums Divisible by 11 (Part 2)

Update: As you can see in my previous post A Two Digit Number and Its Reverse Sums to a Multiple of 11, if you have a two digit number, you can

  • use the reverse of that number to sum together to a multiple of 11.
  • sum the digits to find a factor of the sum.

For example, if one chooses 43 + 34 = 77, one can see that 4+3=7 and 7*11 is 77.

Upon further investigation, I have found that one can use any number whose length is a power of two. This means that not only do 2 digit numbers work in this way, but so do 4 digit numbers, 8 digit numbers, 16 digit numbers, and so on…

However, when one gets to digits larger than 2 (4,8,16), the part about summing the digits to get a factor no longer works. Strangely, that only seems to work on 2 digits.

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