On September 4, 2010, the University of New Mexico lost a football game to the University of Oregon by the score of 72 - 0. The
Albuquerque Journal reported that the Oregon cheerleaders had to do 506 push ups during the game! (The cheerleaders do
cumulative pushups representing the score -- see last month's problem).
If the score was 28 - 0 at the end of the first quarter, 59 - 0 at halftime, 65 - 0 at the end of the third quarter,
and 72 - 0 at the end of the game, can you recreate in order how the scoring took place?
Hints:
(1) Pushups were done only after a touchdown and extra point (7 points)
or a field goal (3 points).
(2) There were no safeties, no missed extra points, and no two point
conversions.
(3) The order in which a team scores a touchdown and a field goal makes a
difference in the number
of push ups the cheerleaders have to do.
Solution to the Problem:
Oregon scored 4 touchdowns in the first quarter; then three touchdowns, a field goal, and a touchdown during the second quarter; then two
field goals in the third quarter; and a touchdown in the 4th quarter.
FG or TD
Push Ups after Score
Total Pushups for the Game
7
7
7
7
14
21
7
21
42
7
28
70
7
35
105
7
42
147
7
49
196
3
52
248
7
59
307
3
62
369
3
65
434
7
72
506
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Rachel Hofer |
Mountain View High School, Mountain View, Wyoming |
| 3. Brandon Preston |
Mountain View High School, Mountain View, Wyoming |
| 4. Ali Torzillo |
Mountain View High School, Mountain View, Wyoming |