perplexus.info :: General : Building a ruler

Building a ruler (Posted on 2008-11-14)

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, I´m 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

Rating: 5.0000 (1 votes)

Solution: (Hide)

5 marks. One of the solutions is below, and I´ll 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.

It´s not the unique solution, I´m 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
Puzzle Thoughts	K Sengupta	2023-02-14 11:11:42
re: 16 cm	Charlie	2008-11-17 13:13:39
re: 16 cm --- thus...	pcbouhid	2008-11-16 16:48:21
16 cm	monica	2008-11-16 14:33:06
Golomb Rulers	Brian Smith	2008-11-16 00:32:35
just 2 remarks	Ady TZIDON	2008-11-15 11:11:26
re: Catch?	Dej Mar	2008-11-14 23:48:22
Difficulty / Unique solutions	ed bottemiller	2008-11-14 19:58:21
re: Catch?	Gamer	2008-11-14 18:33:08
solution	Charlie	2008-11-14 18:06:03
Catch?	ed bottemiller	2008-11-14 17:35:35

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