BrainTwister #80 Iccanobif numbers

#80 Iccanobif numbers

Set by Peter Rowlett

Iccanobif numbers are formed by following this procedure: reverse the digits of the two previous terms and add the resulting numbers together. The first two terms are 1, 1.

These numbers match the Fibonacci sequence for the first few terms. After how many terms do the sequences first differ?

There are two terms with four digits. What are they?

Unlike Fibonacci, each Iccanobif number isn’t necessarily bigger than the previous one. When do they first decrease?

Solution next week

#79 Hamming it up

Solution

The distance between 01011 and 01100 is 3. The smallest number starting with 01 with a distance of 3 from 00000 is 01011. The smallest number starting with 10 with a distance of ≥3 from 00000 and 01011 is 10101. The smallest number starting with 11 with a distance of ≥ 3 from 00000, 01011 and 10101 is 11110.

For a sixth bit, add a 0 or 1 so you always have an even number of 0s and an even number of 1s, producing, for example, 000000, 010111, 101011 and 111100. Alternatively, you can make there be an odd number of each.