Dice stack - Revision history

Oscarlevin at 01:09, 15 July 2013

2013-07-15T01:09:38Z

← Older revision		Revision as of 19:09, 14 July 2013
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	{{Hint \| You need to know that the sides of a regular six-sided die are arranged so that opposite sides always sum to seven. Now consider all the possibilities.}}		{{Hint \| You need to know that the sides of a regular six-sided die are arranged so that opposite sides always sum to seven. Now consider all the possibilities.}}

	{{Answer \| 6}}		{{Answer \| 6}}

	{{Solution \| The sides touching between the bottom and middle dice must be 2 and 3, in some order (it cannot be 1 and 4, since the bottom die has 1 facing out, and if 1 was facing down on the middle die, then 6 would be facing up and this cannot be since the sum between the middle and top die must be 5). It must be that the bottom die has 2 up, since if the middle die had 2 down, then it would have 5 up, making the sum between the middle and top die impossible. Thus the middle die is positioned with 3 down, so 4 facing up. The top die then must have 1 facing down, which makes 6 facing up.}}		{{Solution \| The sides touching between the bottom and middle dice must be 2 and 3, in some order (it cannot be 1 and 4, since the bottom die has 1 facing out, and if 1 was facing down on the middle die, then 6 would be facing up and this cannot be since the sum between the middle and top die must be 5). It must be that the bottom die has 2 up, since if the middle die had 2 down, then it would have 5 up, making the sum between the middle and top die impossible. Thus the middle die is positioned with 3 down, so 4 facing up. The top die then must have 1 facing down, which makes 6 facing up.}}

Oscarlevin at 04:14, 8 July 2013

2013-07-08T04:14:22Z

← Older revision		Revision as of 22:14, 7 July 2013
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			[[File:Oxygen480-actions-roll.svg\|right\|150px]]

	Here is a puzzle from one of the Professor Layton games.		Here is a puzzle from one of the Professor Layton games.

	== Puzzle==		== Puzzle==
	~~[[File:Oxygen480-actions-roll.svg\|right\|150px]]~~
	You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die should be positioned so that the single dot is facing out, towards you. The only other condition as that whenever two dice touch, the numbers on the touching sides must sum to 5. What number will be on the top of the top-most die?		You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die should be positioned so that the single dot is facing out, towards you. The only other condition as that whenever two dice touch, the numbers on the touching sides must sum to 5. What number will be on the top of the top-most die?

Oscarlevin at 04:13, 8 July 2013

2013-07-08T04:13:34Z

← Older revision		Revision as of 22:13, 7 July 2013
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	== Puzzle==		== Puzzle==
			[[File:Oxygen480-actions-roll.svg\|right\|150px]]
	You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die should be positioned so that the single dot is facing out, towards you. The only other condition as that whenever two dice touch, the numbers on the touching sides must sum to 5. What number will be on the top of the top-most die?		You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die should be positioned so that the single dot is facing out, towards you. The only other condition as that whenever two dice touch, the numbers on the touching sides must sum to 5. What number will be on the top of the top-most die?

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	== Extensions ==		== Extensions ==

	How far can this idea go? Could you do something similar with more dice? ~~{{Needs work}}~~		How far can this idea go? Could you do something similar with more dice?

	== References ==		== References ==

Oscarlevin at 01:57, 21 December 2010

2010-12-21T01:57:17Z

← Older revision		Revision as of 19:57, 20 December 2010
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	{{Professor Layton 2}}		{{Professor Layton 2}}

	[[Category: Logic ~~puzzle~~]]		[[Category: Logic puzzles]]
	[[Category: Arithmetic]]		[[Category: Arithmetic]]
	[[Category: Cases]]		[[Category: Cases]]

	__NOTOC__		__NOTOC__

Oscarlevin: Created page with "Here is a puzzle from one of the Professor Layton games. == Puzzle== You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die shoul..."

2010-12-21T01:56:01Z

Created page with "Here is a puzzle from one of the Professor Layton games. == Puzzle== You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die shoul..."

New page

Here is a puzzle from one of the Professor Layton games.

== Puzzle==

You have three regular six-sided dice. You are to stack the dice in a single column. The bottom die should be positioned so that the single dot is facing out, towards you. The only other condition as that whenever two dice touch, the numbers on the touching sides must sum to 5. What number will be on the top of the top-most die?

== Help ==

{{Hint | You need to know that the sides of a regular six-sided die are arranged so that opposite sides always sum to seven. Now consider all the possibilities.}}
{{Answer | 6}}
{{Solution | The sides touching between the bottom and middle dice must be 2 and 3, in some order (it cannot be 1 and 4, since the bottom die has 1 facing out, and if 1 was facing down on the middle die, then 6 would be facing up and this cannot be since the sum between the middle and top die must be 5). It must be that the bottom die has 2 up, since if the middle die had 2 down, then it would have 5 up, making the sum between the middle and top die impossible. Thus the middle die is positioned with 3 down, so 4 facing up. The top die then must have 1 facing down, which makes 6 facing up.}}

== Extensions ==

How far can this idea go? Could you do something similar with more dice? {{Needs work}}

== References ==

{{Professor Layton 2}}

[[Category: Logic puzzle]]
[[Category: Arithmetic]]
[[Category: Cases]]

__NOTOC__