Jump to content
BrainDen.com - Brain Teasers
  • 0
TimeSpaceLightForce

Orienting Dice Tower

Question

Using 1x1x1 dice, Marco makes the tallest dice tower (one die on top of another) 
where the front,back,left and right side do not have same dice face.
How many std dice shall he need?  (a) 3      (b) 4     ( c) 5     (d) 6     (e) 7
Edited by TimeSpaceLightForce

Share this post


Link to post
Share on other sites

5 answers to this question

  • 0

6?

 

 

The answer is six.

Consider the four numbers of each die on the side faces of the tower

taken in ccw order starting with the front.

A tower can be built for each orientation of the top die,

namely 1 2 6 5, 1 5 6 2, 1 4 6 3 and 1 3 6 4:

1 2 6 5 - 1 5 6 2 - 1 4 6 3 - 1 3 6 4 <- top die

2 3 5 4 - 2 4 5 3 - 2 1 5 6 - 2 6 5 1

3 1 4 6 - 3 6 4 1 - 3 5 4 2 - 3 2 4 5

4 5 3 2 - 4 2 3 5 - 4 6 3 1 - 4 1 3 6

5 6 2 1 - 5 1 2 6 - 5 3 2 4 - 5 4 2 3

6 4 1 3 - 6 3 1 4 - 6 2 1 5 - 6 5 1 2 <- bottom die

 

You found them 

Share this post


Link to post
Share on other sites
  • 0

It's at least four - let the 1-spot be the top face and just rotate the die.
And it's at most six - all six numbers appearing on each side.
But can that be done? Not if we begin with 1-spot four times on top.
Each number has to appear once in each position (top, bottom, four sides.)

Share this post


Link to post
Share on other sites
  • 0

The answer is six.

Consider the four numbers of each die on the side faces of the tower

taken in ccw order starting with the front.

A tower can be built for each orientation of the top die,

namely 1 2 6 5, 1 5 6 2, 1 4 6 3 and 1 3 6 4:

1 2 6 5 - 1 5 6 2 - 1 4 6 3 - 1 3 6 4 <- top die

2 3 5 4 - 2 4 5 3 - 2 1 5 6 - 2 6 5 1

3 1 4 6 - 3 6 4 1 - 3 5 4 2 - 3 2 4 5

4 5 3 2 - 4 2 3 5 - 4 6 3 1 - 4 1 3 6

5 6 2 1 - 5 1 2 6 - 5 3 2 4 - 5 4 2 3

6 4 1 3 - 6 3 1 4 - 6 2 1 5 - 6 5 1 2 <- bottom die

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

  • Recently Browsing   0 members

    No registered users viewing this page.

×