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Note: The reason that I picked this one to self-answer was because it was a few weeks (months?) before the Wisconsin State Journal stopped printing Kenken puzzles. This was also the newest Kenken from the Wisconsin State Journal that I was able to access on the internet. There also doesn’t seem to be any descriptions online on how to solve it.

Is there a logical way to deduce the solution to the “Challenging” Kenken in the Wisconsin State Journal from April 26, 2021?

enter image description here

+----+----+----+----+----+----+
|1-  |5-  |4   |10x           |
+    +    +----+----+----+----+
|    |    |7+  |5-  |13+      |
+----+----+    +    +----+    +
|80x |3   |    |    |1-  |    |
+    +----+----+----+    +----+
|         |3÷  |2-  |    |3+  |
+----+----+    +    +----+    +
|5-  |13+ |    |    |4   |    |
+    +    +----+----+----+----+
|    |         |2÷       |3   |
+----+----+----+----+----+----+

$\endgroup$

4

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  1. Fill in the numbers that do not have a +, -, x, or ÷:

enter image description here

  1. Note that there is only one way to get 5-, and using this information, we can put 1/6 in the 3 5- boxes and then logically deduce the 2÷ (mostly because I kept hitting dead ends later on if I put a 1 in that box) (note that the 5 in R1C3 should be a 4 – I fixed that in this screenshot):

enter image description here

  1. Now take the ways we can multiply to 80 – this will help us solve the 80x box: We have
+---------+---------------------------+
|80x using|Ways to do it (no using 1*)|
+---------+---------------------------+
|1 number |             80            |
+---------+---------------------------+
|2 numbers|    2*40,4*20,5*16,8*10    |
+---------+---------------------------+
|3 numbers|     2*20*2,...,4*5*4      |
+---------+---------------------------+

The way to multiply to 80 with 3 numbers that doesn’t cause any contradictions later on is 4*5*4 (which is legal because there are no boxes that confine numbers to a specific area, except for the boxes. It’s only required that the 1-6 are unique in each column and row).

This forces a 4 in R2C6 and then (which I forgot to do earlier) we can deduce that the 3+ must be 1 and 2 in some order (only two unique numbers that add up to 3), so now our grid is

enter image description here

  1. To get to 10x with 3 numbers, we must have 5*2*1 in some order. We know that the 2 must be in R1C4 due to Kenken rules, forcing 1 in R1C5 and 5 in R1C6. Then, 2 is forced in R2C1, and so on and so on. Our breakthrough allows us to fill in a bunch of new numbers.

enter image description here

  1. Finally, note that R4C5 and R3C5 must be 6 and 5 respectively. Only then we can fill in R4C4 and R5C4 without running into a contradiction, and then the rest of the grid is trivial, with a final unique solution:

enter image description here

+----+----+----+----+----+----+    +---+---+---+---+---+---+
|1-  |5-  |4   |10x           |    | 3 | 6 | 4 | 2 | 1 | 5 |
+    +    +----+----+----+----+    +---+---+---+---+---+---+
|    |    |7+  |5-  |13+      |    | 2 | 1 | 5 | 6 | 3 | 4 |
+----+----+    +    +----+    +    +---+---+---+---+---+---+
|80x |3   |    |    |1-  |    |    | 4 | 3 | 2 | 1 | 5 | 6 |
+    +----+----+----+    +----+    +---+---+---+---+---+---+
|         |3÷  |2-  |    |3+  |    | 5 | 4 | 1 | 3 | 6 | 2 |
+----+----+    +    +----+    +    +---+---+---+---+---+---+
|5-  |13+ |    |    |4   |    |    | 6 | 2 | 3 | 5 | 4 | 1 |
+    +    +----+----+----+----+    +---+---+---+---+---+---+
|    |         |2÷       |3   |    | 1 | 5 | 6 | 4 | 2 | 3 |
+----+----+----+----+----+----+    +---+---+---+---+---+---+

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