Last month, I was introduced to a new game at my son-in-law's Super Bowl Party. My son-in-law creates games to keep those who
could care less about a particular sporting event interested in the game.
In this game, he had a 10 x 10 grid on poster paper with the digits from 0 to 9 along the top and 0 to 9 along the side
(see below). On the left side, he put the name of one of the teams (like Philadelphia) and on the top he put the name of the other
team (like New England).
Each person at the party took turns putting their initials in one of the squares. This continues until all of the squares are filled in unless the
number of party-goers does not divide evenly into 100; then there will be some blank squares. For example, if there are 25 people at the party,
each person will have their initials in 4 squares; if there are 8 people at the party, then each person will have their initials in 12 squares and there
will be four squares left blank.
The digits represent the units digit of the score for each team. So, the scores 0, 10, 20, 30, and 80 would all be the same in this game:
they would all be represented by 0. Similarly, the scores 7, 17, 27, 37, and 57 would all be represented by the digit 7.
My son-in-law gives prizes to the person whose initials are in the square for the scores at the end of each quarter. At this party, he gave out
$5 after the 1st quarter, $10 at halftime, $5 after the third quarter, and $20 at the end of the game.
At our party, we put the Philadelphia Eagles along the left side and the New England Patriots at the top. Here is how it played out last month:
After 1st quarter: Eagles 9 Patriots 3, so the person whose initials were in the bottom row (9) and the fourth column (3) won the money.
After 2nd quarter: Eagles 22 Patriots 12, so the person whose initials were in the third row (2) and the third column (2) won the money.
After third quarter: Eagles 29 Patriots 26, so the person whose initials were in the bottom row (9) and the seventh column (6) won the money.
Final score: Eagles 41 Patriots 33, so the person whose initials were in the second row (1) and the fourth column (3) won the money.
Now, here is the problem of the month:
Mr. P wants to know what are the best squares and the best individual digits based on the past 52 Super Bowls.
You should download a copy of the game sheet and fill in the winning teams' scores on the left side and the losing teams' scores on the top.
Click here to download the Game Sheet
Click here to download a copy of the results of the 52 Super Bowls
Now answer the following questions based on your findings. You may first want to determine the total number
of times each units digit occurs in a score (for questions 2 and 3).
(1) Which two squares on the chart were the most frequently landed on?
You may give your answer as a coordinate pair like (3, 2).
(2) Which are the top four units digits that Mr. P should pick?
Make certain that you add up the digits from both the winning and losing teams. This is just a single digit, not a square from the chart.
(3) Which three units digits should you not pick?
Solution to the Problem:
From the data in the chart below, the answers are:(1) The coordinates (1, 7) and (4, 7) each occurred three times.
(2) The four most frequently occurring digits are:
7: 20 times
4: 15 times
1: 14 times
0: 13 times
(3) The three digits that you should not pick are:
2: 4 times
5: 5 times
8: 6 times
Correctly solved by:
| 1. Faith Pfeifer |
Mountain View High School, Mountain View, Wyoming |
| 2. Emilee Benedict |
Mountain View High School, Mountain View, Wyoming |
| 3. Linzy Carpenter |
Mountain View High School, Mountain View, Wyoming |
| 4. Hope Pfeifer |
Mountain View High School, Mountain View, Wyoming |
| 5. Bryce Villanueva | Victoria, Minnesota |
| 6. Frankie Jenkins |
Mountain View High School, Mountain View, Wyoming |
| 7. Ivy Joseph | Pune, Maharashtra, India |
| 8. Rob Miles | Northbrook, Illinois |
| 9. Kimberly Howe | Vienna, Virginia |