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Old 03-19-2012, 01:55 AM
zenobia43 zenobia43 is offline
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Join Date: Mar 2012
Posts: 114
Default Missed constraint

OK I think I got it. I can derive the missing constraint from the grid.

If we label the grid category blocks like this:

AB AC AD
DB DC
CB

where A is weekday, B is first name, C is holiday, and D is gum,

we can see in DB (bold text in previous reply) that Maxwell can only be: {spearmint, tropical fruit}. I.e. we could pick either gum choice for Maxwell. One of the choices will lead to the solution.

From CB (also in bold text in the previous reply), we can see that Maxwell can only be {Flag Day, Halloween}.

If we pick Maxwell = spearmint in DB, the constraints in DC will imply that Maxwell can only be {Valentines Day, Yom Kippur}.

This conflicts with the constraints in CB. I.e. combining the constraints in CB and DC, all of the holidays are X'd out. So Maxwell cannot = spearmint. We can place a red X at the intersection of Maxwell and spearmint gum.

If we pick Maxwell = tropical fruit in DB, combining the constraints in CB and DC leave us with {Flag Day, Halloween}. As long as there is at least one possibility left for Maxwell, it is a valid choice.

Since there were only two choices left: {spearmint, tropical fruit}, and we eliminated spearmint, then tropical fruit is the only remaining choice.

Picking tropical fruit for Maxwell will lead to Nicolas = cinnamon = Tuesday = Flag Day. The rest is routine.

The moral of this story is that after doing all the normal tricks to find constraints, one can look at category blocks (AC and DB are the easiest for me) that only have a few choices left. Check each open cell to see what the implications would be in the adjacent blocks if the open cell had a green circle in it. If putting a green circle in an empty cell would result in a null set for a category, then a red X belongs in that cell.

Last edited by zenobia43; 03-29-2012 at 05:12 AM.
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