Logic Masters Deutschland e.V.

To Christmas 2022 some eager puzzlefriends have again arranged a group in which everybody had to make anonymously a puzzle for someone else. These puzzles are now presented one after the other here in the portal.

It was late December, as Santa and his gnomes were preparing for the busiest time of the year: Christmas, when millions of gifts to millions of children around the world were delivered! It was pretty delicate work, and the logistic preparations were almost complete for the festive season. Almost, as there was one problem: An earthquake had hit the shores of Indonesia pretty recently, which triggered a catastrophic eruption on Krakatoa! This caused a major shift in tectonic plates, and now the islands around the Krakatoa were not placed on where the older maps claimed them to be. Understanding the urgency of the situation, Santa called one of his most reliable gnomes, Lupo, to solve this dilemma for him. When Lupo came, Santa began his explanation: “The situation is dire. Everything we know about the area is completely unreliable. Thankfully, all hope is not lost, as I was able to get one of your fellow gnomes to scout the area beforehand as much as they can. They came back with the following points:

• The effects of the earthquake are pretty massive. In the aftermath of the ripple, all islands are now relatively apart from each other, and some islands have split in two such that there aren’t any islands left which are larger than size 9 anymore.
• Each island still has houses numbered 1 to n, which is equivalent to the size of the hill each house sits on.
• Because of the eruption and the remaining particles, only a few houses were able to send back some limited information about themselves. These houses provided information about how many cells they could see looking downhill in the indicated directions combined, where their vision was blocked by higher houses or Krakatoa, and couldn’t see anything behind those higher houses.
• Our gnome friend has flown around the entire area and took notes about how many distinct islands were visible from certain points inward. They also repeated this process by flowing straight to heart of Krakatoa, and looking outwards, and noted how many islands were visible from next to the volcano. In both these measurements, higher houses blocked the vision of shorter houses behind them.”

As Santa was finishing up his explanation, he took out a big parchment and laid it down on the table. “Here is all the information gathered.”, he said. As Lupo leaned in, his confusion grew even further: “...Dear Santa, are you sure this is the right map? I do not see any of those numerical values you talked about!”
“See, that’s why I called you. Our dear gnome friend has either removed most of the information, or ciphered them so that I can present them to you. They think it’s funny when they can spell out your name on parchments like this. And they turned the entire volcano into a playground too, so you have to figure those digits on yourself. But they at least ensured to me that there was a method to their madness. You can find them all here.”, as Santa took a smaller piece of paper out of his pocket. It looked like a list of bullet points to Lupo. “I see. And may I ask, who is this gnome friend of ours that likes to play around this much?” “Well, they said that if you complete this map for me, there might be a clue inside about who they might be. Which is a good incentive for you to solve this as quickly as you can, eh Lupo? Hundreds of children’s happiness depends on you!”

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