Logic Masters Deutschland e.V.

Difficult decision - the last one of the 2013 Wichtel puzzles

In December Santa Claus' helpers always have an unbelievable heap of work to deal with. Wishing lists have to be scanned, orders have to be placed in the christmas workshops and wrapping paper has to be selected.

On the morning of December 20th a gnome and an elf had finished most of their tasks and allowed themselves a rest at the warm fireplace, each of them with a cup of hot chocolate. They really deserved it. "Well", said the elf sipping pleasurably his hot drink. "This year everything went very well. But, gnome, I'd really like kind of a bigger challenge. Something tricky, you know?" "Yeah, dear elf, I know exactly what you mean", answered the gnome and pushed his cap from his left to his right ear. "Ho, ho, ho", came from the door, where suddenly stood Santa Claus. "Then I have the right thing for you", he said and took a slip of paper out of a pocket of his red smoking jacket. "Here I have a wish of a dear earth child. Well, actually these are nine wishes and as you might guess I can't decide, which one to fulfill. That's a piece of work for you, isn't it?" "Let's see", said the gnome and took the paper from Santa Claus. The elf curiously bend forward in order to get a glimpse at it. "Now", said the gnome, "we just make all the nine of it."

"How do you fancy this, dear gnome?" asked Santa Claus. "Yay!" exclaimed the elf, "I already have an idea." He placed his cup onto the small table and went away to get pencil and paper. When he arrived back the gnome and the elf put their heads together and were unaccessible for anybody.

Late in the evening the three of them met again and examined the result. "O dear!", muttered Santa Claus. "How might this be solvable? There aren't any hints given." "Look out, dear Santa, I going to explain it to you:

Kropki: Here you have to enter the numbers 1 to 7. In the bottom row there are some numbers that are important for the Kakuro. These are marked with an arrow.

Tapa: Here you find some cells with questions marks. Each question marks stands for a number. And all these numbers - and only these numbers - are relevant for the puzzles below the Tapa. Two questions marks in one cell give two different hints.

Kakuro: The cells with question marks are important for the Japanese sums. Only this sums may occur in the Japanese sums. Additionally you have the numbers from the Tapa.

ABCD: This puzzle contains only the letters A,B,C. How many belong in a row or column has to be derived from the Tapa and the Japanese sums. The bottom four rows of this puzzle are the hints for the underground puzzle. The letters have to be replaced by numbers. I don't remember, which letters stands for which number. The elf has told me the combinations, but you know my weak memory. The numbers to the left have to be taken from the magnets.

Japanese sums: The hints are the question marks in the Kakuro and the Tapa. Besides the numbers in the rightmost three columns are relevant for the ABCD puzzle. But only the ones marked with a question mark. That's very important. Numbers in the other cells have to be ignored for the ABCD.

Starbattle: This is apparently not unique. But in connection with the magnets it should become unique. The distances between the stars in the first five rows are transferred into the cells left to the magnets. Exactly in this order. The distances between the stars in the columns are valid for the columns of the magnets. Some of them are + and some -."

"Wait a moment, dear elf", said Santa Claus, „How is this star distance thing meant?" The elf thought briefly while the gnome pushed his cap from his right to his left ear and scratched his chin. "These are the numbers of cells between the stars, dear Santa.

Magnets: The hints are taken from the Starbattle, so for each row and column exactly one number. I just can't remember, whether you have to put each number into the negative or the positive field. You have to figure out the other values. Well, one lonesome cell is given. Apart from that it is totally ignored.

Koralle: Here the numbers have to be taken from the Kropki. I think, that's everything important.

Phew!", said the gnome and leaned back.

"Okay", said Santa Claus, "now I'm really curious about what all this may lead to. And whether the whole thing has one solution. But I know that some of our gnomes are much more competent than me in figuring such things out. All right, folks, then let's go to bed, the next days are going to be very exhausting."

Each of the three sipped placidly one more glogg - of course without alcohol - and went to bed satisfied.