## Sum of the sum

For fans of Kakuro

### Sum of the sum

Here's another kakuro idea. Instead of giving the sum of the digits in the word, give the sum of the digits of the sum of the digits.

For example, if the "sum of the sum" is 7, the sum itself could be either 7, 16, 25, 34, or 43.

Would some of you programming geniuses like to try your hand at composing such a puzzle?

Bill Smythe
Smythe Dakota

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Joined: 11 February 2006

### Re: Sum of the sum

Smythe Dakota wrote:Here's another kakuro idea. Instead of giving the sum of the digits in the word, give the sum of the digits of the sum of the digits.

For example, if the "sum of the sum" is 7, the sum itself could be either 7, 16, 25, 34, or 43.

Would some of you programming geniuses like to try your hand at composing such a puzzle?

Bill Smythe

Hi Bill,
Sorry for the late answer, but I'm not watching this forum on a regular basis.

Creating such puzzles (let's call them SS-Kakuros) from valid (*) classical Kakuros is straightforward in theory: merely replace all the given sums by the corresponding sums of the sums and filter the result for uniqueness.
Notice that any valid SS-Kakuro can be obtained by such a process, so this is not restrictive. However, nothing guarantees that the puzzle thus obtained from a valid Kakuro is a valid SS-Kakuro (in general, it will probably not have a unique solution). As a result, you may have to try many Kakuros before you find a valid SS-Kakuro (this is the purpose of filtering).
I suspect that valid SS-Kakuros are a rarity (so, this may be the challenge: find valid ones).

Now, about solving. As for any puzzle, you have to suppose the given SS-Kakuro is valid, which means that there is one and only one set of sums (i.e. one and only one classical Kakuro) compatible with the given sums of sums.
One obvious strategy is trying to solve all the potential Kakuros compatible with the given sums of sums. Only one will have a solution.
Of course, this would be very tedious. So, unless there appears to be some opportunity for finding shortcuts (parts of solutions common to several possibilities for sums), I don't foresee much fun in the game.

* : valid = one and only one solution
denis_berthier
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