MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C785BA.46D84BA0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C785BA.46D84BA0 Content-Location: file:///C:/753AC875/2007prob5.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Problem 5

Problem 5<= /b>

 

A g= ame is played where teams gain either 4 points or 7 points when they score. No oth= er point values are possible. Therefore, it would clearly be impossible to get exactly 5 points in this game. What is the highest total score that CANNOT = be obtained?

 

[Problem submitted b= y Don Hentschel, LACC Professor of Mathematics.]=

 

 

 

Solution for Prob= lem 5:

 =

Sta= rt by filling in a table of possible scores. Once we get four numbers in a row (1= 8, 19, 20, 21), all greater values are possible by adding 4’s to these numbers. Therefore, 17 is the highest score that cannot be obtained.

 

4’s<= /p>

7’s<= /p>

Total

1

0

4

0

1

7

2

0

8

1

1

11

3

0

12

0

2

14

2

1

15

4

0

16

1

2

18

3

1

Four in a row!
 
19

5

0

20

0

3

21

 

 

=

 

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