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#1
03-16-2012, 11:29 PM
 zenobia43 Senior Member Join Date: Mar 2012 Posts: 175
Need help on tough? one

When I get stuck, it's usually because I've misplaced or forgotten to place an X. I'm hoping that's the case with the following puzzle I had to solve by trying two alternatives to see which one ran into a conflict. I would like to find out how to solve this just from the clues and pattern of constraints in the grid.

The category labels are as follows:

Mon - Tues - Wed - Thurs - Fri
Franklin - Katherine - Maxwell - Nicolas - Stephanie
Flag Day - Halloween - New Years - Valentines Day - Yom Kippur
bubblegum - cinnamon - peppermint - spearmint - tropical fruit

The clues:

1. The person who chewed the spearmint gum isn’t planning ahead for Flag Day.
2. The person who’s making plans for New Years chewed the peppermint gum.
3. Either Stephanie or Katherine arrived on Monday.
4. Of the person who chewed peppermint gum and Katherine, one is making plans for Valentine’s Day and the other arrived on Friday.
5. The person who’s making plans for Yom Kippur arrived some time before Stephanie.
6. The person who arrived on Tuesday didn’t chew the tropical fruit gum.
7. Of Nicolas and the person who’s making plans for Halloween, one chewed the cinnamon gum and the other chewed the tropical fruit gum.
8. The five individuals are the person who’s making plans for Yom Kippur, the person who arrived on Tuesday, Maxwell, the person who chewed the bubble gum, and the person who’s making plans for New Years.
9. The person who’s making plans for Yom Kippur arrived the day after the person who’s making plans for Halloween.

After following all the normal procedures, I get to the following state:

Mon - Katherine - VD - {bubb, spear}
Tues - {Frank, Nic} - {FD, Hall} - cinnamon
Wed - {Frank, Max, Nic} - {Hall, YK} - {spear, trop}
Thurs - {Frank, Max, Nic, Steph} - {FD, YK} - {bubb, spear, trop}
Fri - {Frank, Steph} - New Years - peppermint

bubblegum - {Frank, Katherine, Steph} - {FD, VD}
cinnamon - {Frank, Nic} - {FD, Hall}
peppermint - {Frank, Steph} - New Years
spear - {Frank, Katherine, Max} - {VD, YK}
trop - {Frank, Max, Nic, Steph} - {FD, Hall, YK}

FD - {Frank, Max, Nic, Steph}
Hall - {Frank, Max}
New Years - {Frank, Steph}
VD - Katherine
YK - {Frank, Nic}

I found the solution by trying each of the two gum choices for Monday. Monday seemed to be the most constrained, so I started there. One of the choices results in a conflict, and the other results in the solution.

I also noticed that in the holiday category, there are only two outcomes. For example, picking either of the remaining holidays on Tuesday will determine the holidays for Wednesday and Thursday. Only one of the choices can be the solution. Maybe that would be a better category to work on next.

Sure seems like I've missed (or misplaced) a constraint somewhere.

Thanks

Last edited by zenobia43; 03-29-2012 at 01:33 AM.

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