GeekDad Puzzle of the Week Solution – Functional Numeric Wordsearch

Reading Time: 2 minutes

This past week’s puzzle:

Max and Nora really enjoy the “wordsearch” puzzles from our favorite local BBQ restaurant. Within a grid of letters, they have to find each listed word looking horizontally, vertically, or diagonally. Sometimes, as a trick, the word is spelled backwards to throw off younger spellers – and the backwards diagonals are the worst!

This week’s GeekDad Puzzle of the Week is based upon finding things within a grid, but instead of letters the grid is made completely out of numbers from 1 to 9.

numbergrid

Within this grid, this week’s challenge is to find the set of 5 numbers in a contiguous row, column, or diagonal that have the highest and lowest output values from the function:
gridformula

For example, looking at the digits “3 5 1 2 5”, the output would be (3 + 5) 1 – (2 x 5) or -2… a little chilly for a temperature reading, but probably not the highest or lowest value sets in the overall grid.

In addition to the two extremes (maximum and minimum), please list the total count of “zero” values output from the grid. Looking at the digits “3 7 2 4 5”, the output would be (3 + 7) 2 – (4 x 5) = 0.

The “trick” in this week’s puzzle is that the function, above, is not “symmetric.” that is, f(3,5,1,2,5) = -2 does not necessarily equal f(5,2,1,5,3) = -8. So for each set of 5 numbers in the traditional word search direction (horizontal, vertical, two diagonals) would have to be calculated in each direction to determine the maximum and minimum overall values, as well as finding all of the “zero” values to count them.

Congratulations to Sergio Garcia, who found the following local extrema:
Maximum value : 158 = f(9,9,9,1,4)
Minimum value : -79 = f(1,1,1,9,9)
Number of 0s : 118

Sergio’s response was selected at random from all of the correct (or reasonably correct) submissions sent in over the past week.

Special thanks to Randy Slavey who provided the following diagram identifying each of the values above.
numeric_search_solution

Thanks to everyone that submitted a response. Happy puzzling!

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