From the first row you can see that f(0,y) = 3y
From the first column you can see that f(x,1) = 3-2x
From the second column it's clear that f(x,2) = 6-2x, and so forth.

At some point it's evident, and the other values so confirm, that f(x,y) = 3y-2x.

OK that's the idea. A 2-diminsional "what's the next term in this sequence" puzzle.
Only we don't ask the next term, we ask for the simplest function that generates the given terms.

See if this one is too easy (there are plenty of clues in the table):

Suppose I conjure a function

f(,x).yI give you a matrix of

fvalues for= {0 1 2 3 4 5 6} andx= {1 2 3 4 5 6}.yIt looks like this:

\x| 1 2 3 4 5 6y---+------------------

0 | 3 6 9 12 15 18

1 | 1 4 7 10 13 16

2 | -1 2 5 8 11 14

3 | -3 0 3 6 9 12

4 | -5 -2 1 4 7 10

5 | -7 -4 -1 2 5 8

6 | -9 -6 -3 0 3 6

From the first row you can see that

f(0,) = 3yyFrom the first column you can see that

f(,1) = 3-2xxFrom the second column it's clear that

f(,2) = 6-2x, and so forth.xAt some point it's evident, and the other values so confirm, that

f(,x) = 3y-2y.xOK that's the idea. A 2-diminsional "what's the next term in this sequence" puzzle.

Only we don't ask the next term, we ask for the simplest function that generates the given terms.

See if this one is too easy (there are plenty of clues in the table):

Same range of values for

andxas above.y\x| 1 2 3 4 5 6y---+--------------------------

0 | 1 1 1 1 1 1

1 | 0 1 2 3 4 5

2 | -1 0 1 0 -7 -28

3 | -2 -1 0 -17 -118 -513

4 | -3 0 17 0 -399 -2800

5 | -4 7 118 399 0 -7849

6 | -5 28 513 2800 7849 0

What is

f(,x)?yIf you like this puzzle type, then let the solver make one, and we'll keep the thread going.

Aligning a table like this is easy: just use Courier font.

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