1995 IMC solutions
1 E
2 C
3 D
4 E
5 A
6 B
7 C
8 B
9 D
10 A
11 E
12 D
13 C
14 E
15 B
16 A
17 A
18 C
19 C
20 D
21 D
22 E
23 B
24 B
25 A
Hints:
21. Half the procession takes 22 1/2 minutes. So Gill goes to the end and back in 22.5 minutes. Assuming constant speed it takes 11.25 minutes to meet the last band. At the start of Gill's trip the last band is 1.5 km away. In 11.25 minutes, they travel 0.375 miles forward. So Gill has travelled (1.5-0.375)*2=2.25 miles in 22.5 minutes. Therefore speed=6 mph.
22. 4 ways of getting to the point that is the corner of the blank square from the start. From there 4 ways to get to the finish. So 4x4=16 ways of getting from X to Y via the inside and using the top half. 1 way using the outside alone. Symmetrical, so double the routes we've found so far =2x(16+1)=34
24. Join the radius of the incentre to A and B. You have two triangles, the sum of their altitudes is p.
25. Top left view of the cube is the bottom view rotated 180 degrees about the face with the I on it. So in the top left view, F would be the bottom face. Making a model helps!