How We Derived the Table from Medved's Figures

In my original article, I compared Medved's selective information presentation to one of Martin Gardner's math puzzles. I don't think I could call myself a proper geek unless I gave it a thorough Martin Gardner try.

Medved's statements describe the top ten and twenty films for the 1980s, separated into four ratings categories (G, PG, R and Other). We can begin with an empty chart-- and for convenience, I've given each cell a varibale name, A, B, C, etc. Remember that the upper two rows must add up to 10 films each, and the bottom row adds up to 20.

"•   Looking over Variety's list of the Top 10 box office films of the decade of the 1980s only one-- Beverly Hills Cop-- happened to be rated R, even though R films accounted for more than 60 percent of all titles released in this period."

This means that C = 1.

"•    At the same time, PG films represented less than 25 percent of all titles-- but occupied six of the top 10 places on the list of the decade's leading moneymakers."

This means that B = 6.

Since the total (A+B+C+D) is 10, and B+C=7, we also know that A+D=3. Therefore, neither A nor D can be greater than 3.

"•    If you expand the calculations to consider the twenty leading titles in terms of domestic box-office returns between 1981 and 1990, 55 percent were rated G or PG; only 25 percent were R films."

55 percent of the twenty-film total is 11 films. Therefore, I+J=11.

Since B=6, and B+F=J, we can assume that J must be between 6 and 11. F must be between 0 and 5.

Since I+J=11, and J lies in the range 6-11, then the variable I must be between 0 and 5. (That is, if J is 11, then F is 5, but if J is 6, then F is zero.)

The 25 percent of films that were rated R is a total of 5 films-- thus, K=5.

If C+G=K, then we know that G=4.

We can now determine the number of "Other"-rated films among the top 20 earners (L).

If I+J+K=16, and I+J+K+L=20, then L=4.

If L(4)=D+H, and D is a value between 0 and 3, then H must be between 1 and 4.

Since J must lie between 6 and 11, and and I+J=11, then I could be as little as zero, or as great as 5.

Can we derive a value for E? Possibly. The sum of E+F+G+H is 10, so the sum of E+F+H is 6. This shows that E=6-(F+H).

The most that F+H can be is 6. If the most that H can be is 4, then the most that F can be is 2.

This means that J cannot be more than 8.

This also means that I cannot be less than 3.

Thus, the value for E lies between 0 and 2.

If we recheck the second row, we find that if we assume the largest values for E and F-- 2-- and add in G, that gives us 2+2+4=8. Thus, H cannot be less than 2.

This also limits D to being no more than 2.

Let's look at the first row. A+D must add up to 3. D cannot be greater than 2, so therefore, A cannot be less than 1.

This is as far as simple math logic can take us. Now that we've reduced many of the variables to ranges of three, and since they're interdependent, we can try substituting values to see if we get any contradictions. New values are bolded.

Assume A=1:

D=2, H=2.

E=2, F=2.

I=3, J=8.

Assume A=2:

D=1, H=3

E+F = 1+2. Cannot resolve which is 1 or 2.

I=3-4, J=7-8

Assume: A=3

D=0, H=4

E+F= 2. Their ranges do not change. Thus, the ranges for I and J do not change either.

In conclusion: as I said in my article, you cannot look at Medved's account of these films and figure out what's going on.

Copyright 2000-6 Brian Siano

(unless otherwise noted)