## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# Mike's Magical Scale

Best Answer Barcallica, 03 June 2013 - 03:37 PM

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

I don't think so. 5,1,1,1 also works. I think these are the only solutions

Go to the full post

10 replies to this topic

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 01 June 2013 - 09:55 PM

Mike has a magic scale, each side of which holds a positive integer.  He plays the following game: each turn, he chooses a positive integer n. He then adds n to the number on the left side of the scale, and multiplies by n the number on the right side of the scale. (For example, if the turn starts with 4 on the left and 6 on the right, and Mike chooses n = 3, then the turn ends with 7 on the left and 18 on the right.) Mike wins if he can make both sides of the scale equal. Show that if the game starts with the left scale holding 17 and the right scale holding 5, then Mike can win the game in 4 or fewer turns.

• 0

### #2 Barcallica

Barcallica

• Members
• 150 posts
• Gender:Male
• Location:Room with a View

Posted 02 June 2013 - 06:55 AM

Spoiler for Is it?

• 0

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 02 June 2013 - 06:39 PM

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?
• 0

### #4 Barcallica

Barcallica

• Members
• 150 posts
• Gender:Male
• Location:Room with a View

Posted 03 June 2013 - 03:37 PM   Best Answer

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

I don't think so. 5,1,1,1 also works. I think these are the only solutions

• 0

### #5 superprismatic

superprismatic

Not just Prismatic

• Moderator
• 1281 posts
• Gender:Male

Posted 04 June 2013 - 09:44 PM

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

I don't think so. 5,1,1,1 also works. I think these are the only solutions

There are two others: 1,5,1,1 and 1,1,5,1.

• 0

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 05 June 2013 - 04:21 AM

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

I don't think so. 5,1,1,1 also works. I think these are the only solutions

There are two others: 1,5,1,1 and 1,1,5,1.

But is there a three number solution?

• 0

### #7 superprismatic

superprismatic

Not just Prismatic

• Moderator
• 1281 posts
• Gender:Male

Posted 06 June 2013 - 01:15 AM

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

I don't think so. 5,1,1,1 also works. I think these are the only solutions

There are two others: 1,5,1,1 and 1,1,5,1.

But is there a three number solution?

No

• 0

### #8 Pickett

Pickett

Senior Member

• Members
• 546 posts
• Gender:Male
• Location:40°N 83°W +/-10'

Posted 06 June 2013 - 01:42 PM

Spoiler for My Findings

• 0

### #9 Pickett

Pickett

Senior Member

• Members
• 546 posts
• Gender:Male
• Location:40°N 83°W +/-10'

Posted 06 June 2013 - 02:00 PM

Spoiler for Quick Note...

• 0

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 13 June 2013 - 12:02 AM

Bonus points for Pickett though for awesome programming talents!

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users