Moomins’problems 11/12

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Moomins’problems Can you help us?

Group B


Problem number 1 Moomintroll on a very large chessboard can move horizontally and vertically by being able to execute three types of commands: - change direction and turn 90 degrees clockwise: command or; - change direction and turn 90 degrees counterclockwise: command a; - change position and move forward in n boxes keeping the same direction: command fn. For example, starting from the box with the arrow> [2,3] and direction to the right (east), with these commands [f4, a, f2, a, f4, a, f4, or, f1] arrives in the box with * [1,1] bottom left. PROBLEM Moomintroll is located in the box [20,20] with direction to the right (east) and must execute the following list of commands [f, a, f, f, f, a, f, f, o, f, f] to go at Too-ticky’s house. Find the coordinates of the house where the path ends and write them down below

X=

Y=



Problem number 2 


L1=

Moomintroll, using the simple cryptography of Julius Caesar, makes riddles for Too-ticky: Find the list L1 obtained by encrypting with key 6 the list that contains in order the letters of the name of the sea that the Romans called "Nostrum". Find the key K with which the list that contains the letters relating to the capital of France becomes [j, u, l, c, a, c]. Given the list [o, l, i, m, p, i, a, d, i] find the corresponding L2 encrypted with a key such that the letter p is encrypted in the letter j. K=

L2=


Problem number 3 Moomintroll decides to draw his family tree (starting from f) described by the following terms: arc (i, l) arc (f, d) arc (m, c) arc (b, h) arc (g, a) arc (f, b) arc (b, m) arc (f, g) arc (l, e) arc (g, j) arc (l, k) arc (f, i) Answer the questions below. Find the L1 list of tree leaves, written alphabetically. Find the L2 list of nodes that have at least 2 children or are uncles, listed alphabetically. Find the L3 list of nodes for which there is at least one brother and each brother has at most one child, listed alphabetically. Find the L4 list of uncles in the tree, listed alphabetically.

L1=

L2=

L3=

L4=


Problem number 4 Someone stole the tray from the wall. There are four possible culprits. They said: Moomintroll: "I'm not the culprit". Little My: "Moomintroll is lying". The squirrel: "Little My is telling the truth". Too-ticky: "Little My stole the jam". Knowing that only one of these four (not necessary the culprit) is lying and the other three are telling the truth find the culprit. Put “M" for Moomintroll, “L" for Little My, “S" for the squirrel and “T" for Too-ticky in the box below.


Correct answers 1. X=19 Y=25 2. L1= S,K,J,O,Z,K,X,X,G,T, K,U K=20 L2=I,F,C,G,J,C,U,X,C 3. L1=C,D,E,H,K L2=B,D,F,G,H,I L3=A,E,H,J,K,M L4=B,D,G,H,I 4. L


Finish That’s funny!

By Mario Motta, Silvio Pellegrino, Federico Romano and Elia


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