# The mess of Adrian Puzzlinger

Adrian Puzzlinger has gone missing again. Even worse, for puzzle lovers, the latest puzzle under construction is a mess. The only shred of order in the chaos of Puzzlinger's puzzler parlor is this puzzling chart, which, predictably, puzzles the perpetually puzzled puzzle police.

                                  _______                               _______
4 _______        9|   | 1 |          _______          25|   | 1 |
2|   | 2 |      18|   | 2 |       32|   | 2 |         50|   | 2 |
3| 1 | 3 |      36| 3 | 4 |       48| 4 | 3 |         75| 5 | 3 |
5|   | 5 |      45|   | 5 |       80|   | 5 |     14 100|   | 4 |
7 ___|___|___|     ___|___|___|      ___|___|___|        ___|___|___|
4|   | 2 |      27|   | 1 |      256|   | 2 |        125|   | 1 |
9| 1 | 3 |     432| 3 | 4 |      576| 4 | 3 |       1125| 5 | 3 |
25|   | 5 |     675|   | 5 |     1600|   | 5 |    23 2000|   | 4 |
10 ___|___|___|     ___|___|___|      ___|___|___|        ___|___|___|
8|   | 2 |      81|   | 1 |     2048|   | 2 |        625|   | 1 |
27| 1 | 3 |    5184| 3 | 4 |     6912| 4 | 3 |      16875| 5 | 3 |
125|   | 5 |   10125|   | 5 |    32000|   | 5 |   32 40000|   | 4 |
13 ___|___|___|     ___|___|___|      ___|___|___|        ___|___|___|
16|   | 2 |     243|   | 1 |    16384|   | 2 |       3125|   | 1 |
81| 1 | 3 |   62208| 3 | 4 |    82944| 4 | 3 |     253125| 5 | 3 |
625|   | 5 |  151875|   | 5 |   640000|   | 5 |  41 800000|   | 4 |
|___|___|        |___|___|         |___|___|           |___|___|


What kind of puzzle was Adrian making?

As this kind of puzzle has assumed different aliases, the authorities need a full description of how Adrian used this chart, not just a name.

Other missing-puzzler case

• Is the diagonal important? It seems that if for each row/column, the number on the far left is the number in the middle^(row+1)*the number on the right^row. For example the 253125 = 5^(4+1)*3^4 – qwertylpc Jun 30 '16 at 18:07
• I suggest that it may be better to think of the exponents as coming from the columns rather than the rows (which is why the boxes are offset in the way they are). Not because I think I know the answer, for the avoidance of doubt; just because it explains the peculiar layout. – Gareth McCaughan Jul 1 '16 at 11:02
• Essential data: $\tiny \begin{array}{|c|c|} \hline\raise5mu\strut 1 & 2~~ \\ & 3~~ \\ & 5~~ \\ \hline \end{array} \begin{array}{|c|c|} \hline\raise5mu\strut 3 & 1~~ \\ & \!\!\!(2) \\ & 4~~ \\ & 5~~ \\ \hline \end{array} \begin{array}{|c|c|} \hline\raise5mu\strut 4 & 2~~ \\ & 3~~ \\ & 5~~ \\ \hline \end{array} \begin{array}{|c|c|} \hline\raise5mu\strut 5 & 1~~ \\ & \!\!\!(2) \\ & 3~~ \\ & 4~~ \\ \hline \end{array} ~$ Layout and other numbers are just additional clues. This is a regular kind of puzzle in newspapers worldwide. – humn Jul 2 '16 at 21:30
• It's a crossword? – Mithical Jul 5 '16 at 8:45
• ........Sudoku? – Mithical Jul 5 '16 at 8:58

With credit to Dan Russel for identifying the puzzle involved, Adrian appears to be

identifying the numbers which, if put in the top left hand corner of a multiplicative, staircase-shaped cage within a 5x5 KenKen puzzle, would mean that just two distinct numbers are used in that cage. By staircase-shaped cages, I mean one of the following (or their reflections/rotations):

 __ __
|   __|
|__|

__ __
__|   __|
|   __|
|__|

__ __
__|   __|
__|   __|
|   __|
|__|
__ __
__|   __|
__|   __|
__|   __|
|   __|
|__|


Each row of the chart refers to one of the above shapes (and the layout of the chart points to the staircase shapes).

For example, the second row, second column(/diagonal) of the chart), 27 432 675 | 3 | 1 4 5 means that

if we see 27, 432 or 675 as the multiplicative total of a cage like the second one I drew above, then we know that there are three 3's along the main diagonal. Additionally if the number is, say 675, then we know that there are two 5's in the other cells.

Notably, the missing 1's 2's and 4's in the chart are where

it would be impossible to tell whether there are two 2's or a 1 and a 4.

The additional numbers, 4 7 10 13 and 14 23 32 41 are

the minimum/maximum sums of the above cages and are put next to their respective products. eg 41 is from five 5's along the main diagonal and four 4's in the other cells (41=5*5+4*4) and is put next to 800000 (=5^5*4^4).

• You explained every clue, and caught the nuance that this is for a less-common sized board! (Might want to also explicitly mention that these numbers effectively are multi-cell freebies, like a number in a single-cell cage.) The system won't allow the bounty to be delivered yet, but this solution deserves more attention and ^votes in the meanwhile anyway. – humn Nov 3 '16 at 17:58
• Nice job figuring this one out! Couldn't wrap my head around it. – Dan Russell Nov 3 '16 at 19:51

I'll take a leap and say it's Sudoku. Why?

1.)

This is a regular kind of puzzle in newspapers worldwide. – humn

And since I was informed that it wasn't a crossword, that leads to Sudoku. :P

2.) There are boxes with empty spaces in it, and the numbers in each box do not repeat, nor overlap with the box adjacent to it.

3.)

As this kind of puzzle has assumed different aliases,

Sudoku is also known as 'su doku' or 'number place'.

• All the reasoning here is valid and only one detail seems susceptible to being extrapolated in a way that is not in accord with the actual mystery puzzle. – humn Jul 6 '16 at 22:16
• And what about all those products in the chart? – humn Sep 19 '16 at 21:08

KenKen puzzle.

The offset rows/columns with the numbers 1-5 are suggestive because

the same number never appears in the same box or column, implying that each number must be used once per permutation.

Also, based on the numbers outside of the boxes,

it appears there is some higher-order math going on here, like multiplication, and in a KenKen puzzle you can have addition, subtraction, multiplication, and division. This is unlike Sudoku which does not involve mathematical operations.

I can't quite discern exactly what Adrian was doing with the outside-the-box numbers, but my best guess is that it has to do with

The number of possible ways of cluing sets of numbers, or the number of possible solutions given a set of numbers and a box/condition.

• Your last sentence has all the right words but could be rephrased, mixed with a couple of concepts brought forward from earlier and an adjective not yet mentioned, for a concisely definitive conclusion. (To fully detail that conclusion is easy but slightly tedious, and I'd be glad to add that later.) Thank you for breathing life back into this puzzle. – humn Oct 27 '16 at 20:22
• @humn Yeah, I suspected that I was headed down the right path, then took a wrong turn into the weeds. Perhaps someone smarter will see the question's bump and put 2 and 2 together. – Dan Russell Oct 27 '16 at 20:37

(Wikified worksheet— feel free to correct or add.)

Sums and products decomposed:                                                       _______
5^2 |   | 1 |
2 5^2 |   | 2 |
_______                               3 5^2 | 5 | 3 |
1+3  _______        3^2 |   | 1 |              _______         4 5^2 |   | 4 |
2 |   | 2 |     2 3^2 |   | 2 |       2 4^2 |   | 2 |      5+9     |   |   |
3 | 1 | 3 |     4 3^2 | 3 | 4 |       3 4^2 | 4 | 3 |           ___|___|___|
5 |   | 5 |     5 3^2 |   | 5 |       5 4^2 |   | 5 |      5^3 |   | 1 |
1+3*2  ___|___|___|        ___|___|___|          ___|___|___|  3^2 5^3 | 5 | 3 |
2^2 |   | 2 |       3^3 |   | 1 |     2^2 4^3 |   | 2 |      4^2 5^3 |   | 4 |
3^2 | 1 | 3 |   4^2 3^3 | 3 | 4 |     3^2 4^3 | 4 | 3 |    5+9*2     |   |   |
5^2 |   | 5 |   5^2 3^3 |   | 5 |     5^2 4^3 |   | 5 |           ___|___|___|
1+3*3  ___|___|___|        ___|___|___|          ___|___|___|      5^4 |   | 1 |
2^3 |   | 2 |       3^4 |   | 1 |     2^3 4^4 |   | 2 |      3^3 5^4 | 5 | 3 |
3^3 | 1 | 3 |   4^3 3^4 | 3 | 4 |     3^3 4^4 | 4 | 3 |      4^3 5^4 |   | 4 |
5^3 |   | 5 |   5^3 3^4 |   | 5 |     5^3 4^4 |   | 5 |    5+9*3     |   |   |
1+3*4  ___|___|___|        ___|___|___|          ___|___|___|           ___|___|___|
2^4 |   | 2 |       3^5 |   | 1 |     2^4 4^5 |   | 2 |          5^5 |   | 1 |
3^4 | 1 | 3 |   4^4 3^5 | 3 | 4 |     3^4 4^5 | 4 | 3 |      3^4 5^5 | 5 | 3 |
5^4 |   | 5 |   5^4 3^5 |   | 5 |     5^4 4^5 |   | 5 |      4^4 5^5 |   | 4 |
|___|___|           |___|___|             |___|___|    5+9*4     |___|___|