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Solutions 2021

Here are the answers to the 2021 MATH+ Advent Calendar challenges. The detailed solutions can be found in the Challenge Archive.

  1. Trip Planning:
    6. 308,515
  2. Heads or Tails:
    8. 0.85 < p ≤ 0.90 holds.
  3. Cinnamon Stars:
    6. The maximal number is M = 72.
  4. Sawmill:
    10. All four parts of the work schedule are feasible.
  5. Soccer:
    10. Winterfield lost against Coldbury and played draw against Glacierhampton.
  6. T-shirts:
    5.  The largest possible number of pixies with a red T-shirt is 11.
  7. Kandinsky:
    6. The third digit behind the decimal point is 6.
  8. Gingerbread:
    6. Set 2 and 7.
  9. Two Rooks:
    4. The blue rook stands either on a8 or f3.
  10. Santa’s Snowflake-powered Snowmobiles:
    7. 7
  11. Christmas Bauble Mashup:
    8. (b) \tfrac{1}{4}, (c) \tfrac{35}{128}.
  12. Black Ice:
    8. Between 175 and 180 minutes.
  13. Mondrian:
    4.  The largest possible number of 2×2 squares is 17.
  14. Auguste, the Christmas Goose:
    6. With the best strategy, the children find Auguste in the worst case on 20 December.
  15. Magic Ribbons:
    4. Ribbon no. 4.
  16. Reindeer Election:
    8. Dancer, Dasher, Blitzen, Comet, Rudolph.
  17. The Eggnogg Chocolate Egg:
    3. Annelie should make the first move, taking three nougat eggs.
  18. Hat Challenge 2021:
    9. 68 ≤ M ≤ 72.
  19. Casino:
    8. Roughly 288 €.
  20. Thieves in the Snow:
    3. The cat was first, but the fawn ate the cucumber slices. The beaver stole the carrot.
  21. Tetrahedron:
    6. At time T = 4:36 pm.
  22. Zelda in Distress:
    Unfortunately, there was an error in this task. Therefore, it was not possible to find a solution. We are very sorry!
  23. Traces in the Snow:
    2. Basima bets, “The number 2.517.849.199 is hit.”
  24. Tempting Vanilla Crescents:
    5. 85