PDA

View Full Version : Need help on tough? one

zenobia43
03-16-2012, 11:29 PM
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

zenobia43
03-19-2012, 01:55 AM
OK I think I got it. I can derive the missing constraint from the grid.

If we label the grid category blocks like this:

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.