Today we want to count smurfs (蓝精灵). This is how it works:

0. We start with the ordinary numbers from 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …

1. Then we replace every 4th number by “smurf” according to its multiplicity (几次):

  1, 2, 3, smurf, 5, 6, 7, 2-smurf, 9, 10, 11, 3-smurf, 13, 14, 15, ...

3. 16 is smurf-smurf.

0. The numbers

Probably you remember the for loop, that allows us to count, like this:

This is a re-introduction. This time I wrote it for C++ and in English, hence CE.

Once you have set up a programming environment, you can try to write a first small program.

The Goal

Today’s goal is a multiplication table (乘法表) as follows:

   1  2  3  4  5  6  7  8  9 10
   2  4  6  8 10 12 14 16 18 20
   3  6  9 12 15 18 21 24 27 30
   4  8 12 16 20 24 28 32 36 40
   5 10 15 20 25 30 35 40 45 50
   6 12 18 24 30 36 42 48 54 60
   7 14 21 28 35 42 49 56 63 70
   8 16 24 32 40 48 56 64 72 80
   9 18 27 36 45 54 63 72 81 90
  10 20 30 40 50 60 70 80 90 100

In words: The 10 rows (行) contain the multiples of the corresponding number. In every row the number, then its double (两次), then the triple (三次), …, the 10-fold (十次).