Task 1: "Digits Sum

You are given two positive numbers $N and $S.

Write a script to list all positive numbers having exactly $N digits
where sum of all digits equals to $S.

Example

Input:
    $N = 2
    $S = 4

Output:
    13, 22, 31, 40
"

My notes: sounds like fun.


Task 2: "Palindrome Partition

You are given a string $S. Write a script print all possible partitions
that gives Palindrome. Return -1 if none found.

Please make sure, partition should not overlap. For example, for given
string "abaab", the partition "aba" and "baab" would not be valid,
since they overlap.

Example 1

Input: $S = 'aabaab'
Ouput:
 There are 3 possible solutions.
 a) 'aabaa'
 b) 'aa', 'baab'
 c) 'aba'

Example 2

Input: $S = 'abbaba'
Output:
 There are 3 possible solutions.
 a) 'abba'
 b) 'bb', 'aba'
 c) 'bab'
"

My notes: hang on, what exactly do we mean by a "partition"?  this isn't clear!

First: isn't a single letter a substring - an element - of a partition?
presumably not - otherwise 'a', 'a', 'b', 'a', 'a', 'b' would be a solution
to the first example.  So presumably each partitioned substring is of
minimum length 2.

Second: Do all the substrings in a partition have to "span" the string, i.e.
do all the substrings in a partition have to append together to form the
original string?  Presumably not, otherwise 'aabaa' would not be a solution to
the first example.

Third: Can there be more than two elements in a single partition of a string?
None of the examples show more than two.  I don't know the answer to this one,
so I'll assume that "there can only one or two elements in a partition".

So this problem is badly specified.  Let's assume that we mean:

"A partition of a string S is either a single substring of minimum length 2
or a pair of exactly 2 non-overlapping substrings of S, each of minimum length
2.  Find all partitions of S for which the partition substring(s) are all
palindromes."

If this isn't the right definition, well damn it, the question should have
been clearer - and I expect full marks!

Having programmed the above, this also claims (for example) that "aa" is a
possible solution to example 1 - which is fair enough by the above statement.
So I tried adding the logic:
- find the single substrings that are palindromes, call that @p1
- find the pairs of non-overlapping substrings where each substring is
  a palindrome, call that @p2
- remove from @p1 any element that is one of any pair in @p2

But even this shows 4 solutions for example 1:

aabaa
aba
aa,baab
aa,aa

(whereas only the first 3 are expected).  I guess we are saying that aa,aa
should not a solution because aa,baab is (and baab contains aa)?  I can't
be bothered to implement this, as the deal is: we implement the problems
given to us; not we first debug the problem specs given to us and then
implement the debugged spec.  Please make the problem spec clearer next
week, Mohammed!