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Apples Plus Bananas

by Andrew He, Nicholai Dimov, and Sophie Mori

Answer:
HARVEST FESTIVAL

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€œyour total cannot be reduced”, 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
🍎APPLES3104RoHo 36153H
πŸ₯‘AVOCADOS4046Hass2A
🍌BANANAS4236Red1R
🫘BEANS4528Fava/Broad3V
🫐BERRIES4240Blueberries10E
πŸ₯¦BROCCOLI3082Crowns6S
πŸ†EGGPLANT (AUBERGINE)4602White4T
πŸ‡GRAPES3451Sugrathirtyfour12F
πŸ₯KIWIFRUIT3279Golden5E
πŸ‹LEMONS3617Seedless7S
πŸ₯­MANGO3363Kensington Pride8T
πŸ‘PEACHES4399Indian4I
πŸŽƒPUMPKIN3131Decorative (Painted)9V
🍊TANGERINES/MANDARINS3389Satsuma2A
πŸ…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 πŸ‹, there is exactly 1 prime number PLU code associated with lemons. Therefore, lemons must be 3617.
  2. With this information, πŸŒπŸ‹ has a unique solution with 🍌 = 4236.
  3. Similarly, πŸ‹πŸ‹πŸ‘ has a unique solution for peaches.
  4. Knowing the value of peaches gives a unique solution for the broccoli in πŸ₯¦πŸ‘.
  5. Blueberries (🫐) have a single PLU code of 4240, under the commodity BERRIES.
  6. Now, πŸ«πŸ«πŸ«πŸ«πŸ‡ and πŸ«πŸ«πŸ«πŸ«πŸ‡πŸ‘πŸ‘ force a unique solution for grapes.
  7. Using this, πŸ†πŸ‡ has a unique solution for eggplants.
  8. From πŸŽƒπŸŽƒπŸŽƒπŸŽƒπŸŠ, the code for the 🍊 must be odd. Looking at 🫘🫐πŸ₯¦πŸ₯¦πŸ₯¦πŸ₯¦πŸ‡πŸ‡πŸŠ tells us that the code for 🫘 is even. In 🫘🫘πŸ₯¦πŸ†πŸ‡πŸ‡πŸ‡πŸ‡πŸ‡πŸ‡πŸ‡, 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 🍊 and πŸŽƒ. Fittingly, the pumpkin variety is Decorative, just like a jack-o'-lantern.
  10. πŸ‹πŸ₯­πŸŽƒ and πŸ₯­πŸ₯­πŸŽƒ give a unique solution for mangoes.
  11. πŸ₯‘πŸ«πŸ₯­πŸ₯­πŸŽƒ gives a unique solution for avocados.
  12. πŸ₯πŸŽƒπŸ… and πŸ₯πŸ₯πŸ‹πŸŽƒπŸ… give unique solutions for tomatoes and kiwifruit.
  13. 🍎πŸ₯‘πŸ₯­ and 🍎πŸ₯πŸ₯­πŸ₯­ give unique solutions for apples.
  14. The row πŸŽπŸ†πŸ†πŸ₯πŸ‹πŸ…πŸ…πŸ… 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 πŸ₯¬ (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.