The challenge this week is as follows: given an alphanumeric string of arbitrary length in A1, derive a single formula to return the number of numbers within that string which are divisible by *either* 3, 5 or 7.

By “divisible” here I mean of course that there is no remainder after division.

And by “numbers within that string” I mean all *consecutive* substrings of any length within that string which may be interpreted as a number. (It can also safely be assumed that there are no alphanumeric combinations within the string in A1 which would be interpreted by Excel as numeric, e.g. JAN01.)

For example, the string:

XX**30**X**5**XXX**42**XX**771**

contains, by this definition, 13 numbers: 3, 0, 30, 5, 4, 2, 42, 7, 7, 1, 77, 71 and 771.

The answer for the above string would be 9, since:

3 **IS** divisible by 3

0 **IS** divisible by 3, 5 and 7

30 **IS** divisible by 3 or 5

5 **IS** divisible by 5

4 **IS NOT** divisible by any of 3, 5 or 7

2 **IS NOT** divisible by any of 3, 5 or 7

42 **IS** divisible by 3 or 7

7 **IS** divisible by 7

7 **IS** divisible by 7

1 **IS NOT** divisible by any of 3, 5 or 7

77 **IS** divisible by 7

71 **IS NOT** divisible by any of 3, 5 or 7

771 **IS** divisible by 3

Solution next week. Best of luck!