Spatial: Sticky-Sided Dice (Hard)

**Benny** · 07-07-2006, 12:47 AM

Competition ends on Monday 31st July 2006 at midnight UK time.

Benny will donate 1000 tokens to the first person who posts the correct solution and explanation to the following problem:

This problem is identical to Spatial: Sticky-Sided Dice (Easy), except that two faces can only be stuck together if their spots total 7. :twisted:

**Hyno** · 07-07-2006, 01:09 AM

G=120
L=56

How did I go this time? ;-)

**mrmojorisin** · 07-07-2006, 09:28 AM

G = 119
L = 84

Cheers,
M

**salocius** · 07-07-2006, 10:47 AM

Damn, too late. Just come out of meeting.

I get the same figures as mr mojorisin.

**Benny** · 07-07-2006, 01:35 PM

Well my best answers were:

L=84
G=119

So let's see how you got your answers Hyno :!: :?:

**Hyno** · 08-07-2006, 08:36 AM

You guys are right. I made an error with the first one & did the maths for 6 dice with the second one.

That's what you get for rushing things.

ops:

**Benny** · 08-07-2006, 09:38 AM

Quote:

Originally Posted by mrmojorisin

G = 119
L = 84

Can you give your explanation now?

**mrmojorisin** · 09-07-2006, 12:29 PM

the opposite sides of a regular dice add up to seven. So no matter how you stack them up (assuming the sides stuck together add up to seven), the open sides will always total to a multiple of seven. It also doesnt matter which sides you stick in this case, since they all add up to seven.

The lowest total will obviously again come from arranging them as a large cube. This cube has 12 pairs of dice faces. Each pair adds up to seven. So the total is 7x12 = 84.

The highest total comes from exposing the maximum number of faces - arranging them in a straight line. In this case, there are 17 pairs of dice faces exposed. So the total is 7x17 = 119.

Cheers,
M

**Benny** · 09-07-2006, 01:12 PM

That's great - thanks! Tokens on their way

Not as difficult as I'd anticipated, after all!

ops:

07-07-2006, 12:47 AM	#1 (permalink)
Benny Super Duper Poster Join Date: Mar 2004 Location: UK Posts: 604 Credits: 1,247 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	Spatial: Sticky-Sided Dice (Hard) Competition ends on Monday 31st July 2006 at midnight UK time. Benny will donate 1000 tokens to the first person who posts the correct solution and explanation to the following problem: This problem is identical to Spatial: Sticky-Sided Dice (Easy), except that two faces can only be stuck together if their spots total 7. :twisted:

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07-07-2006, 01:09 AM	#2 (permalink)
Hyno Super Duper Poster Join Date: Jul 2005 Location: Wollongong, Australia Posts: 747 Credits: 2,251 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	G=120 L=56 How did I go this time? ;-)

07-07-2006, 09:28 AM	#3 (permalink)
mrmojorisin Regular Poster Join Date: Mar 2006 Posts: 77 Credits: 319 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	G = 119 L = 84 Cheers, M

07-07-2006, 10:47 AM	#4 (permalink)
salocius Super Poster Join Date: Feb 2006 Location: Gatwick, UK Posts: 214 Credits: 617 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	Damn, too late. Just come out of meeting. I get the same figures as mr mojorisin.

07-07-2006, 01:35 PM	#5 (permalink)
Benny Super Duper Poster Join Date: Mar 2004 Location: UK Posts: 604 Credits: 1,247 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	Well my best answers were: L=84 G=119 So let's see how you got your answers Hyno :!: :?:

08-07-2006, 08:36 AM	#6 (permalink)
Hyno Super Duper Poster Join Date: Jul 2005 Location: Wollongong, Australia Posts: 747 Credits: 2,251 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	You guys are right. I made an error with the first one & did the maths for 6 dice with the second one. That's what you get for rushing things. ops:

09-07-2006, 12:29 PM	#8 (permalink)
mrmojorisin Regular Poster Join Date: Mar 2006 Posts: 77 Credits: 319 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	the opposite sides of a regular dice add up to seven. So no matter how you stack them up (assuming the sides stuck together add up to seven), the open sides will always total to a multiple of seven. It also doesnt matter which sides you stick in this case, since they all add up to seven. The lowest total will obviously again come from arranging them as a large cube. This cube has 12 pairs of dice faces. Each pair adds up to seven. So the total is 7x12 = 84. The highest total comes from exposing the maximum number of faces - arranging them in a straight line. In this case, there are 17 pairs of dice faces exposed. So the total is 7x17 = 119. Cheers, M

09-07-2006, 01:12 PM	#9 (permalink)
Benny Super Duper Poster Join Date: Mar 2004 Location: UK Posts: 604 Credits: 1,247 Nominated 0 Times in 0 Posts TOTW/F/M Award(s): 0	That's great - thanks! Tokens on their way Not as difficult as I'd anticipated, after all! ops:

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