Tricks with 11.

We have been discussing multiplying and dividing by 11 (and x + 1) in our articles in this newsletter for the past several issues. Let us take a break by discussing some tricks with the number 11.

Ask someone to give you a two-digit number, for example 35.

You can immediately give them multiples of 11.

1. Reverse the digits of the given number and attach it in front or at the back: 5335 and 3553 are multiple of 11.

• Split the reversed number into two addends and attach one in front and the other at the back or both in front or both in the back of the number in any order.
• If you use (53 = 32 + 21), then the following are multiples of 11: 323521, 213532, 322135, 213235, 353221 and 352132.
• If you use (53 = 41 + 12), then the following are multiples of 11: 413512, 123541, 411235, 124135, 354112 and 351241.

• Get the 9s complement of 35 which is 64  and attach it in front or at the back of the number. 3564 and 6435 are not only multiples of 11 but also 99.

You can also split 64 into two or more addends and attach them as shown in #2 above to the original number Try getting the complement of 35 from other numbers, for example its 7s complement is 42. 3542 and 4235 are also multiples of 11.