MMM2019 Solutions.pdf
(1.35 MB, PDF)
… he has taken more steps to the left, we know that after some number of steps, say p 2 {2, 4, . . . , 22} we have that for the last time he has taken exactly the same number of steps to the left as to the right. Now consider dance d̂, that is the ‘complement’ of dance d in the sense that at all steps until step p it takes a step in the opposite direction of dance d and after step p the steps are in the same direction as dance d. An example (for an eight-step dance): If d = RRLLLRLL, then p = 6, … Answer to Problem 5: ‘Goes out one ear and into the other’ Question (a): When viewed from the front, the situation is as follows. Working in centimeters, the diameter of the sphere equals p 136, so that r = p 34. From the center point C to the point B where the brim of the party hat touches the head of the garden gnome right above the left ear, the distance is also equal to r. Since B is in a horizontal plane that is 2 cm above the horizontal plane passing through the two ear holes, the center point … you used the scissors; the point M indicates the center point of the five-pointed star of Maastricht (in the middle!) and the ant is located above the left ear, precisely at the point B 3 on the brim of the hat. On this flat piece of paper you need to compute the length of BM. The points A1 = A2, B, Q, and D, are 4 points that divide the brim of the party hat into 4 equal pieces; Q is right in front. The total length of the brim follows from its radius before cutting the party hat open (see question …