Weihnachtsmann rot

Challenge from 3. December

Sneaky Elves
In an earlier version, we forgot the words "equal" and "equally". Sorry for any inconvinience!

Author: Ariane Beier

Project: MATH+ School Activities

Challenge:

For their good work today, the five sneaky elves Charlie, Kim, Luca, Mika, and Ulli received big box with finitely many, whole, delicious coconut macaroons from Santa himself. Worn out from the exhausting day, they carry the box home and go to bed immediately while yawning loudly. Now, the box sits on the elves' kitchen table, where it is guarded by the elves' dog Anouk.

At 10:34 p.m., Charlie sneaks into the kitchen, gives a macaroon from the box to Anouk, divides the remaining macaroons into five equal parts (while not dividing a single macaroon), pouches one part, rearranges the residual four parts into a big pile, and returns to bed with a cunning grin on the face. At 11:56 p.m., Kim tiptoes into the kitchen, gives a macaroon from the box to Anouk, divides the remaining macaroons into five equal parts (without splitting single macaroons), puts one of theses parts into the pyjama pockets, shoves the other four parts into a pile, and slips off to bed looking very pleased. At 1:45 a.m., 3:17 a.m., and 4:23 a.m., Luca, Mika, and Ulli, respectively, repeat this procedure.

Despite the wakeful night, the elves are in a very good mood at 9:00 a.m. and meet for breakfast. They offer a breakfast macaroon to Anouk and split the remains of the coconut macaroons equally among themselves (again, dividing none of the single macaroons).

How many coconut macaroons does Kim at least get altogether?

Illustration: Frauke Jansen

PDF download

Possible answers:

  1. 35

  2. 352

  3. 3,522

  4. 35,223

  5. 352,230

  6. 3,522,300

  7. 35,223,004

  8. 352.230.042

  9. 3,522,300,421

  10. 35,223,004,219

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