March 2011
Problem of the Month
Push Up Problem
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
|