There is a set of cubes of three different colors: red, blue and yellow and their edges are of integer length.

In the following statements the bold capital letters refer to specific digits with a one-to-one correspondence of digit to letter.

The volume of each red cube is NIL.
The face of each blue cube has NO area.
The volume of each yellow cube is ZERO.
The total volume of all the cubes is NOTHING.

There are NO cubes of one of the colors, and NONE of another.

How many cubes are there of the remaining color, and what is that color?

Missing color: blue, 21413 cubes. After listing a bunch of 2 digit squares and 3 and 4-digit cubes.  I Aligned which could share N's or O's.  After I figured the digits for NO, NIL, and NONE.  I set up an equation below to solve for the # of cubes for the 3rd color.  I used trial and error, and forutnately got

Red volume: 125 (1610)

Blue volume: 64 (21413)

Yellow volume: 4096 (16)

C1*V1+C2V2+C3v3 = NOTHING

<o:p> </o:p>

(NOTHING - C1*V1+C2V2)/V3 = C3
<o:p>
</o:p>
NO = 16, <o:p></o:p>

NONE = 1610<o:p></o:p>

<o:p> </o:p>

NIL: 125<o:p></o:p>

<o:p> </o:p>

ZERO: 4096<o:p></o:p>

<o:p> </o:p>

Z = 4<o:p></o:p>

E = 0<o:p></o:p>

R = 9<o:p></o:p>

O = 6<o:p></o:p>

N = 1<o:p></o:p>

T= 3<o:p></o:p>

H=7<o:p></o:p>

I= 2<o:p></o:p>

L=5<o:p></o:p>

G= 8<o:p></o:p>

<o:p></o:p>

Posted by Cyriis on 2007-11-07 01:39:40