Round 1

P(8 winners at least once) = P(not predicting 8 winners all season) = 0.5 = (1-[P(correct)^8])^22

Solving for P(correct):

P(correct) = 0.64781

The second part is to find the binomial probability of 6 successes in 8 trials for p = 0.64781, which is 0.25668.

This is the probability of predicting exactly 6 winners in a round. Over 22 rounds, that should happen 5.64703 times.

2. The letters in Group 1 are homophones of complete English words.

A = a
B = be, bee
C = see, sea
I = I, eye
J = jay
L = ell (obscure; measurement of about 45 inches)
M = em (obscure; a printer’s measure)
N = en (obscure; another printer’s measure)
O = owe
P = pea
Q = cue, queue
R = are
T = tea
U = you, ewe
Y = why

3. The data concerns our solar system. The row headings are the names of the planets in the solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto.

The column headings should be: the distance from the sun in astronomical units (au), diameter in kilometres, length of day in Earth days, length of year in Earth days.

Recognising the data in row 3 is the secret to solving this puzzle. The 365.26 is quite conspicuous, and the scores of 1 imply ratio scales of some kind.

4. A: 3, 0
B: 3, 270
C: 1, 270
D: 6, 0

Try it out!

5. Throughout history, many people have used revolvers, but there is arguably only one person famous for using a crossbow: William Tell. William Tell was a historical figure who is famed for using a crossbow to shoot an apple off his son’s head. That’s why a crossbow was used to represent him.

William Tell was also the inspiration for Rossini’s William Tell Overture. This piece of music was later used as the theme for the fictional character who is represented by the revolver: The Lone Ranger.

Both men are associated with the same piece of music. A joke went around a few years back, implying that upon hearing the William Tell Overture, sophisticated people think of William Tell, and unsophisticated people think of The Lone Ranger.