Weihnachtsmann rot

Challenge from 10. December

An Ancient Anniversary Gift
19** is a 4-digit year.

Author: Ariane Beier

Project: MATH+ School Activities

Challenge:

For the first time, Elf Horton is responsible for the Christmas decoration of the North Pole's festival hall. Since he was waiting a very long time for this opportunity, Horton is quite excited and wants to do something extraordinary. Thus, he buries himself into the stock, where he browses through decorative items from the past several hundred years. After a while, Horton is quite sure that he has found the perfect piece for the top of the Christmas tree: a Möbius strip made of sheet metal ornamented with amethyst, malachite, and tourmaline. Horton wonders how old this exquisite decoration must be. Thankfully, there is a letter enclosed with it:

My dearest Conny,
on this Monday, our eighth wedding anniversary, I give you this Möbius strip as a symbol of our everlasting love. It is made for you and this special occasion. With endless joy, I remember the weekend day of our wedding on 13 J*** 19**, the beginning of our wonderful journey together.
Love, John.

As you may have noticed, parts of the wedding date are blurred due to the ravages of time. (Of course, the number of *'s does not represent the number of blurred characters...)

Can you still help Horton and figure out how old the Möbius strip is? More precisely, what is the remainder of the digit sum of Conny's and John's wedding date (given as DDMMYYYY), when divided by 10?

Example: If the date would have been 26 December 1937, then the answer would be 1, since
2+6 + 1+2 + 1+9+3+7 = 31 = 3·10 + 1.

Hints:

  • There are 365 days in a non-leap year and 366 days in a leap year.

  • If a year is divisible by 4, then it is a leap year, except if it is divisible by 100, except-except it is also divisible by 400.

    Examples:
    • The year 2004 was a leap year, because 2004 is divisible by 4, but not by 100.
    • The year 2100 will not be a leap year, since 2100 is divisible by 100, but not by 400.
    • The year 2400 will be a leap year, since 2400 is divisible by 400.

Artwork: Friederike Hofmann

PDF download

Possible answers:

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5

  6. 6

  7. 7

  8. 8

  9. 9

  10. 0

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