All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
Building a ruler (Posted on 2008-11-14) Difficulty: 2 of 5
I have an unmarked ruler (AD) of length 6cm. Making two marks in it, one (B) at 1cm from the left end and other (C) at 2cm from the right end, Im able to measure any integer length from 1 to 6 cm:
       +----+-------------+--------+
       A    B             C        D
AB = 1cm / CD = 2cm / BC = 3cm / AC = 4cm / BD = 5cm / AD = 6cm.

If I have an unmarked ruler of length 14cm, what is the minimum number of marks, and where do I have to make them, in order to be able to measure any integer length from 1 to 14cm?

  Submitted by pcbouhid    
No Rating
Solution: (Hide)
5 marks. One of the solutions is below, and Ill explain why I posted this one:
    +------+------+---------+---------+---------+---+
    A      B      C         D         E         F   G
       2      2        3         3         3      1
When I found this puzzle, and analyzing it, I designed a method to mark a ruler of any length.

I started with the 2 appropriate marks I have to make in rulers of length 4, 5 & 6 (two marks):

length 4: 1 - 1 - 2
length 5: 2 - 2 - 1
length 6: 1 - 3 - 2.

From this on, I figured out that all I have to do is to add a segment of 3cm length, to the previous group, and next to the right end, to achieve the next group of rulers. That is:

length 7: 1 - 1 - 3 - 2
length 8: 2 - 2 - 3 - 1
length 9: 1 - 3 - 3 - 2.

To the next group of three lengths, another mark (length 3), always next to the right end:

length 10: 1 - 1 - 3 - 3 - 2
length 11: 2 - 2 - 3 - 3 - 1
length 12: 1 - 3 - 3 - 3 - 2

To the next group:

length 13: 1 - 1 - 3 - 3 - 3 - 2
length 14: 2 - 2 - 3 - 3 - 3 - 1
length 15: 1 - 3 - 3 - 3 - 3 - 2.

And so on, always adding a 3-length segment to the previous group.

Its not the unique solution, Im aware of this, but is a method that I can use with any ruler length.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: 16 cmCharlie2008-11-17 13:13:39
re: 16 cm --- thus...pcbouhid2008-11-16 16:48:21
16 cmmonica2008-11-16 14:33:06
Golomb RulersBrian Smith2008-11-16 00:32:35
Some Thoughtsjust 2 remarksAdy TZIDON2008-11-15 11:11:26
re: Catch?Dej Mar2008-11-14 23:48:22
Difficulty / Unique solutionsed bottemiller2008-11-14 19:58:21
re: Catch?Gamer2008-11-14 18:33:08
SolutionsolutionCharlie2008-11-14 18:06:03
Catch?ed bottemiller2008-11-14 17:35:35
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information