Round 1

by Jason Ross

1. “Football tipping” is a popular competition in Australia. The Australian Football League has 22 rounds of regular season games, with 8 games per round. Players nominate the 8 teams they expect will win that round.

The probability that I will correctly predict a winner of a game is independent and constant. There is exactly a 50% chance that I will correctly predict all 8 winners for a round at least once per regular season.

To 3 decimal places, what is the expected value of the number of times per season I predict exactly 6 winners in a round?

2. The alphabet has been divided into these two groups.

1. A B C I J L M N O P Q R T U Y
2. D E F G H K S V W X Z

Those currently in group 1 definitely belong in that group. It could be argued that some of the letters in group 2 belong in group 1, but most people would place them in group 2.

What is the criterion for admission to group 1?

3. You have found a floppy disk and are trying to identify the data on it. You open up the tab-delimited file and view the following (shown here in comma-separated format):

0.387,4878,58.65,87.97
0.723,12104,243,224.7
1,12756,1,365.26
1.524,6787,1.026,686.98
5.203,142800,0.4083,4331.984
9.539,120660,0.425,10760.559
19.18,51118,0.7458,30681.84
30.06,49528,0.7958,60194.848
39.53,2300,6.39,90474.902

What should the row and column headings be?

4. I have four cubes. The cubes are constructed from the following nets:

The cubes have been placed side by side in a row. They are arranged in the order (from left to right) A, B, C, D. When this row is viewed from front, back, top and bottom, there are always four different colours on display.

Describe a possible front view, in terms of the numerals and the clockwise rotation (in degrees) of the numerals from the upright.

5. I have two weapons mounted on the wall of my billiard room. On one wall, I have a crossbow. On the opposing wall, I have a revolver. It is my idea of a joke, albeit a very subtle one.

There is a plaque underneath the crossbow with the inscription: “Former; fact; sophisticated.”

There is a plaque underneath the revolver with the inscription: “Latter; fiction; unsophisticated.”

What is the link between the two weapons?

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