Snakes are laid out on a plane with the following requirements:
- Each snake has 3 parts: head, middle and tail.
- Each snake is touched by exactly one head, one middle, and one tail.
- Each snake can only touch another snake at most once.
- Each part of a snake must touch a different part of another snake (no
head-head, middle-middle, tail-tail). - The snakes can’t overlap or cross as they are on a plane.
What is the minimum number of snakes that you need?
#1 by Chris Nokleberg on August 22, 2006 - 6:26 pm
I think it takes 8 snakes.
#2 by Chris Nokleberg on August 22, 2006 - 6:45 pm
http://sixlegs.com/misc/snakes.png
You should wait until Friday to post these things you know
#3 by Alan Green on August 23, 2006 - 8:31 pm
Four.
#4 by Patrick Gras on August 25, 2006 - 3:30 am
I also say 4…
#5 by Mike M. on August 25, 2006 - 12:13 pm
I was trying to find solutions to this puzzle because it was puzzling me elsewhere (that is, assuming the author intended to mention 0 is not a valid answer) and I stumbled upon this page.
By the way, Chris – your solution doesn’t work. The third snake from the top (shaped like a ‘<’) has two heads touching him.
#6 by Eugene Kaganovich on August 25, 2006 - 1:31 pm
zero
#7 by Eugene Kaganovich on August 25, 2006 - 1:31 pm
zero
#8 by Lolita on August 26, 2006 - 6:29 am
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#9 by Chris Nokleberg on August 26, 2006 - 9:16 am
Shoot!
Okay then I change my answer to infinity
#10 by Mocky on August 28, 2006 - 12:46 pm
Zero is the easy way out. If you take zero then you miss out on some interesting problem solving.
After reading the rules it becomes immediately obvious there is only a small set of ways a snake can touch its neighbors. For any given snake, as soon as you touch its head to the tail of another you are forcing its middle to touch a head and tail to touch a middle. In fact there are exactly 2 ways for a snake to touch its neighbors.
http://img143.imageshack.us/img143/9196/snakesonaplanewo5.gif
Configuration #1 (C1) C1
#11 by Mocky on August 28, 2006 - 12:47 pm
Zero is the easy way out. If you take zero then you miss out on some interesting problem solving.
After reading the rules it becomes immediately obvious there is only a small set of ways a snake can touch its neighbors. For any given snake, as soon as you touch its head to the tail of another you are forcing its middle to touch a head and tail to touch a middle. In fact there are exactly 2 ways for a snake to touch its neighbors.
http://img143.imageshack.us/img143/9196/snakesonaplanewo5.gif
Configuration #1 (C1) C1
#12 by Alan Green on August 28, 2006 - 7:03 pm
No really, Mocky, four.
Start off with two snakes 1 and 2. Have the tail of snake 1 (T1), touch the Head of snake 2 (H2). Now get snakes 3 and 4, with the head of 3 touching the tail of 4. That gives the following touching pairs:
T1 H2
H3 T4
At this stage, there are two free tails, two free heads and four free middles. If we match up the heads with the tails, that would leave four free middles, so instead, we match the heads and tails to the middles. Given the rules about only being able to touch each other snake once, there aren’t many ways to do that. That gives the following additional pairs:
M1 T4
M2 H3
M3 T2
M4 H1
So that’s all the pairs. You can then draw out the snakes on paper and satisfy yourself that the pairs can touch without the lines crossing.
#13 by Mocky on August 29, 2006 - 5:44 am
That doesn’t work Alan.
T1 H2
H3 T4
M1 T4
M2 H3
M3 T2
M4 H1
You omitted T3 and had T4 twice, so I assume that’s a typo. You also omitted H4 and have H3 touching both T4 and M2.
But the bottom line with only 4 snakes even if you sort out your doubles and omissions is that you’ll break rule #2 (Each snake is touched by exactly one head, one middle, and one tail.)
#14 by Alan Green on September 4, 2006 - 5:35 pm
Mocky,
Yeah, I think you’re right. I fluffed it when I drew my picture.
Alan.