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--- haas:fall2019:c4eng:projects:pctxinfo [2019/08/23 22:11] – [How to access the puzzle in the public directory] wedge
+++ haas:fall2019:c4eng:projects:pctxinfo [2019/08/24 15:29] (current) – [Positive (greater than) number certainties] wedge
@@ Line 86: / Line 86: @@
 lab46:~/src/c4eng/pctX$ submit c4eng pctX pctX.puzzle.key pctX.puzzle.solution
 </cli>
+=====Positive (greater than) number certainties=====
+Finding and isolating patterns amongst the operations taking place can make available to us additional paths of pursuit for solving the puzzles.
+Now, we know that if the top number is greater than ONE of the values being subtracted from it, does it also reveal anything else?
+<code>
+ X
+-Y
+==
+ Z
+</code>
+Let's say we have, from elsewhere in the puzzle, determined that Z << X, but as yet we have not established any connection between Y and X.
+Can we use this to our advantage?
+Yes. Take a look at these examples:
+<code>
+    4    5    9    7
+-3   -1   -3   -2   -3
+==   ==   ==   ==   ==
+    3    2    7    4
+</code>
+As we can see here, in the small sample size of subtractions we've tried, that when the top number is greater than one of the numbers beneath it, BOTH values beneath it are less than the top number.
+Now, from this approach we cannot make any determinations about how the two lower numbers relate to each other, but we can use it to fill in some gaps.
+So, if we know that Z << X, we can ALSO infer that Y << X (we just don't know how Y relates to Z).
+So unless we can find an example that violates this case, we can run with it as a viable approach to take in the letter division puzzles. Tell me: is there a valid combination that violates this?
+=====Less than number certainties=====
+Like the above, but inverted: what if we KNOW that the top number is less than one of the two numbers beneath it? Can we also infer some pattern? Let's see:
+<code>
+ X
+-Y
+==
+ Z
+</code>
+Let's say that we KNOW, from elsewhere in the puzzle, that X << Y. Can we use that to inform us better on how X relates to Z?
+Looking at some examples:
+<code>
+  11  12  13  14
+-6  -9  -7  -4  -8
+==  ==  ==  ==  ==
+   2   5   9   6
+</code>
+As we can see in the examples above, if X is less than Y, X ends up ALSO being less than Z.
+So unless we can find an example that violates this case, we can run with it as a viable approach to take in the letter division puzzles. Tell me: is there a valid combination that violates this?
+Remember: we are dealing with single digit values (with the exception of the top number needing to borrow), so the viable possibilities are limited.
 =====These are fun, can I do more?=====
 Absolutely! My letter division puzzle database can be found here:

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