Author |
Topic: Cricket Scores (Read 528 times) |
|
Passionately Curious
Newbie
Gender: 
Posts: 24
|
 |
Cricket Scores
« on: Jan 24th, 2009, 12:51pm » |
 Quote  Modify
|
I was playing cricket the other day and one of my friends who was playing, being a very talented batsman, was only hitting boundaries. It got me wondering what scores a cricket player could obtain if he only hit boundaries (4's and 6's) and I quickly realized (unless I made a mistake somewhere) that they could obtain any even score except 2.
So...
a) Show that all positive even integers  2 can be written as 4a + 6b for a, b   
b) Show that every positive even integer  16 can be written as 4a + 6b in at least two different ways.
e.g. 20 = 4 * 5 + 6 * 0 = 4 * 2 + 6 * 2
|
|
 IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Cricket Scores
« Reply #1 on: Jan 24th, 2009, 1:56pm » |
Quote Modify
|
for a we can get 4 and 6, and we can just add 4 repeatedly to get all others.
for b we can use 3*4 = 2*6, as long as the number can be written using at least 3 4s, which is the case for every even number 16 or over.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print