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Three 3-digit non leading zero positive base N integers P, Q and R, with P > Q > R, are such that:

  • Q is the geometric mean of P and R, and:
  • P, Q and R can be derived from one another by cyclic permutation of digits.

Determine all possible positive integer values of N < 30 for which this is possible.

(No Solution Yet, 4 Comments) Submitted on 2009-07-04 by K Sengupta   
Difficulty: 4 of 5 Bonus: Unfolding cube (in Shapes) Rating: 3.17
How many unique shapes can you get by unfolding a paper cube?

You can only cut along edges, and the shape must be in one piece and flat. By unique, I mean rotations and reflections don't count.

This problem can be analogized to four dimensions as well. How many unique 3-dimensional shapes can be made by "unfolding" a 4-dimensional hypercube into 8 cubes? This problem is significantly more difficult than the first.

(Solution Posted, 8 Comments) Submitted on 2004-07-22 by Tristan   
Difficulty: 2 of 5Digits 1 to B (in Just Math) Rating: 2.00
Posted on 2009-07-03 by K Sengupta (No Solution Yet, 1 Comments)
Difficulty: 1 of 5An empty problem (in Riddles) Rating: 1.00
Posted on 2009-07-02 by Daniel (No Solution Yet, 3 Comments)
Difficulty: 2 of 5Fly on a cone (in Just Math)
Posted on 2009-07-01 by Bractals (Solution Posted, 1 Comments)
Difficulty: 3 of 53/9, 12/9 and 1/2 (in Numbers)
Posted on 2009-06-30 by Dej Mar (No Solution Yet, 1 Comments)
Difficulty: 2 of 5How much time will you spend? (in Tricks)
Posted on 2009-06-29 by pcbouhid (No Solution Yet, 3 Comments)
Difficulty: 2 of 5Eight-Digit Numbers In Reverse (in Just Math) Rating: 2.50
Posted on 2009-06-28 by K Sengupta (No Solution Yet, 3 Comments)
Difficulty: 3 of 5Pandigital Processed Primes (in Numbers)
Posted on 2009-06-27 by Charlie (Solution Posted, 1 Comments)
Difficulty: 2 of 5Terminating in seven sevens (in Numbers)
Posted on 2009-06-26 by K Sengupta (No Solution Yet, 2 Comments)
Difficulty: 3 of 53x3 Nim (in Games) Rating: 4.20
Posted on 2009-06-25 by Jer (Solution Posted, 24 Comments)
Difficulty: 2 of 5Subtract 1, get a square (in Just Math)
Posted on 2009-06-24 by K Sengupta (No Solution Yet, 4 Comments)
Difficulty: 3 of 5Bounded Sine (in Shapes)
Posted on 2009-06-23 by Jer (No Solution Yet, 2 Comments)
Difficulty: 2 of 5Multiply Sum and Sum of Squares (in Numbers)
Posted on 2009-06-22 by K Sengupta (No Solution Yet, 4 Comments)
Difficulty: 5 of 5Duality (in Cryptography)
Posted on 2009-06-21 by brianjn (No Solution Yet, 2 Comments)
Difficulty: 3 of 5Powering Up The Matrix (in Just Math)
Posted on 2009-06-20 by K Sengupta (No Solution Yet, 3 Comments)

Recently Posted Solutions:
Difficulty: 3 of 5Pandigital Processed Primes (in Numbers)
Submitted By Charlie. Solution posted on 2009-07-04 12:05:00
Difficulty: 2 of 5Fly on a cone (in Just Math)
Submitted By Bractals. Solution posted on 2009-07-01 17:39:14
Difficulty: 3 of 53x3 Nim (in Games)
Submitted By Jer. Solution posted on 2009-07-01 11:40:30
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Submitted By Jer. Solution posted on 2009-06-23 00:06:30
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Submitted By Bractals. Solution posted on 2009-06-19 22:24:28
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