Great POTW Bake-Off

Question

Pepper, Belle, Emerson, and Ralphie have just competed in POTW’s Annual Bake-Off. Pepper, Belle, Emerson, and Ralphie each came in first, second, third, or fourth in the competition. There were no ties. The baker who came in first placed highest and the baker who came in last placed lowest.

Each baker created a different variety of cookie. One baked ginger snaps, one baked sugar cookies, one baked lemon drops, and one baked peppermint crunch cookies. Each baker also presented their baked goods to the judges on a different coloured plate. One on a white plate, one on a red plate, one on a brown plate, and one on a silver plate.

Using the following clues, determine which baker came in first, second, third, and fourth, which baker baked which variety of cookie, and on which plate they presented their baked goods to the judges.

1. The ginger snaps placed higher than the cookies baked by Emerson, but lower than the cookies presented on the brown plate.
2. The cookies baked by Pepper placed directly below the sugar cookies.
3. The cookies presented on the silver plate placed directly above the cookies presented on the red plate. Belle did not present her cookies on the silver plate.
4. The lemon drops were presented on the white plate and did not come in last place.
5. Ralphie did not come in third. The cookies presented on the white plate were not baked by Ralphie.

_{This was a Problem of the Week from the University of Waterloo, Canada, in 2019.}

Answer 1

Final solution

Belle came 1st with lemon drops on a white plate.
Ralphie came 2nd with sugar cookies on a brown plate.
Pepper came 3rd with ginger snaps on a silver plate.
Emerson came 4th with peppermint crunch on a red plate.

Step by step deduction

1. The ginger snaps placed higher than the cookies baked by Emerson, but lower than the cookies presented on the brown plate.

   That means ginger is NOT Emerson, Emerson is NOT brown, ginger is NOT brown, and also ginger is NOT 1st or 4th, Emerson is NOT 1st or 2nd, brown is NOT 3rd or 4th.

2. The cookies baked by Pepper placed directly below the sugar cookies.

   That means Pepper is NOT sugar, Pepper is NOT 1st, sugar is NOT 4th.

3. The cookies presented on the silver plate placed directly above the cookies presented on the red plate. Belle did not present her cookies on the silver plate.

   That means silver is NOT 4th, red is NOT 1st (and Belle is NOT silver).

4. The lemon drops were presented on the white plate and did not come in last place.

5. Ralphie did not come in third. The cookies presented on the white plate were not baked by Ralphie.

   These two clues are both straightforward to interpret on the logic grid.

So far we have:

and we immediately know Peppermint is 4th. Since 4th is not brown or silver, that means Peppermint is not brown or silver, so Peppermint must be red. Now ginger must be silver and sugar must be brown.

We've completed one box of the logic grid, and we can carry over all those correspondences into other boxes to double our information (e.g. Belle is not silver, so Belle is not ginger) to get

Now we know Pepper placed directly below sugar/brown, which is 1st or 2nd, so that means Pepper can't be 4th/peppermint/red. We also know silver/ginger is directly above red/peppermint/4th, i.e.

silver/ginger is 3rd. Therefore Ralphie is not silver/ginger, so now Pepper must be silver/ginger/3rd.

And we know Pepper placed directly below sugar/brown, so

sugar/brown is 2nd, which means lemon/white is 1st. Now we have:

Finally, by elimination we see that

Emerson is 4th/peppermint/red, which enables the rest to be filled in:

Answer 2

Shorter answer:

From 1, the brown plate is either first or second.

Assume it's first.

Silver and Red are adjacent by 3, so we can only have (Brown/White/Silver/Red) and (Brown/Silver/Red/White). The second one violates 4, so the first must be true.
Lemon Drops are second by 4, so from 1 the Ginger Snaps must be third.
Sugar Cookies are first because from 2 they cannot be last, making Peppermint Crunch fourth.
Emerson is fourth by 1, and Pepper is second by 2, so either Ralphie is third (violates 5) or Belle is third and serves on the silver plate (violates 3).

This is a contradiction. Therefore, Brown is second.

Silver and Red are again forced to be third and fourth by 3, making White first.
Lemon Drops are first by 4, and Ginger Snaps are third by 1, so Sugar Cookies are second by 2 and Peppermint Crunch is again fourth.
Emerson is again fourth by 1, Pepper is third by 2, Ralphie is second by 5 and Belle is first.