# Apples Plus Bananas

### by Andrew He, Nicholai Dimov, and Sophie Mori

This puzzle is about the Price Look Up codesΒ of various produce. Each distinct emoji represents a specific variety of the depicted commodity, which is assigned to a unique PLU code. Since βyour total cannot be reducedβ, the sum of the PLU codes for each row is a prime number. This lets us solve for the varieties and corresponding codes for all the emoji.

EmojiCommodityPLU CodeVarietyNumber of OccurrencesExtract Letter
πAPPLES3104RoHo 36153H
πBANANAS4236Red1R
π«BERRIES4240Blueberries10E
π₯¦BROCCOLI3082Crowns6S
πEGGPLANT (AUBERGINE)4602White4T
πGRAPES3451Sugrathirtyfour12F
π₯KIWIFRUIT3279Golden5E
πLEMONS3617Seedless7S
π₯­MANGO3363Kensington Pride8T
πPEACHES4399Indian4I
πPUMPKIN3131Decorative (Painted)9V
πTANGERINES/MANDARINS3389Satsuma2A
πTOMATOES3423Heirloom5L

The emoji rows are sorted by number of produce and alphabetically by commodity name. If we sort the emojis by the commodity name and index the variety name by its number of occurrences in the puzzle, we obtain the final answer HARVEST FESTIVAL.

## Appendix

Here is a possible method to get all of the PLU codes. We expect most teams to solve the first few manually and write code for the rest.

1. Looking at π, there is exactly 1 prime number PLU code associated with lemons. Therefore, lemons must be 3617.
2. With this information, ππ has a unique solution with π = 4236.
3. Similarly, πππ has a unique solution for peaches.
4. Knowing the value of peaches gives a unique solution for the broccoli in π₯¦π.
5. Blueberries (π«) have a single PLU code of 4240, under the commodity BERRIES.
6. Now, π«π«π«π«π and π«π«π«π«πππ force a unique solution for grapes.
7. Using this, ππ has a unique solution for eggplants.
8. From πππππ, the code for the π must be odd. Looking at π«π«π₯¦π₯¦π₯¦π₯¦πππ tells us that the code for π« is even. In π«π«π₯¦ππππππππ, the only possible choices for the beans are 4528 and 4531, so we take the even one.
9. Using the same rows, we get unique solutions for π and π. Fittingly, the pumpkin variety is Decorative, just like a jack-o'-lantern.
10. ππ₯­π and π₯­π₯­π give a unique solution for mangoes.
11. π₯π«π₯­π₯­π gives a unique solution for avocados.
12. π₯ππ and π₯π₯πππ give unique solutions for tomatoes and kiwifruit.
13. ππ₯π₯­ and ππ₯π₯­π₯­ give unique solutions for apples.
14. The row ππππ₯ππππ is unused in this solve path, but it can serve as confirmation of the codes obtained so far or as a subtle indication that the number of times each emoji occurs is important.

## Authors' Notes

An earlier version of this puzzle used π₯¬ (for CABBAGE). Furthermore, two of the PLU codes needed to use the prefixes for GMO or organic produce. Thankfully, the solution was not unique, so we had the opportunity to rewrite this puzzle to be cleaner.