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Unknown Digits (Posted on 2004-08-11) Difficulty: 4 of 5
In this cryptarithm, each letter above the line represents a digit differing by 1 from the digit represented by the same letter below the line. For example, if A=3 above the line, then A=2 or A=4 below the line. All occurrences of a letter on the same side of a line represent the same digit. It is also known that there are total of five digits in the solution.
 ADABA
+CACBA
------
 DBABC

See The Solution Submitted by Brian Smith    
Rating: 3.6667 (3 votes)

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Other Reasoning | Comment 6 of 9 |

I agree the answer is

  56505+15105=71610

(Upper letters upper case, lower letters lower case): A=5; B=0; C=1; D=6; a=6; b=1; c=0; d=7

The ones column gives a small set of relationships between A, c, a, and C (since A=a+/-1 likewise for C).

The 100s and 10,000s columns give a set of relationships between A, C, a, and d (and c, D). Combining with 1's column, there are only 16 possibilities (power of 2 - cool):

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BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>d</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>3</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>8</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>8</TD></TR></TBODY></TABLE>

The 10's column has 4 sets for B and b:

<TABLE style="WIDTH: 100pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=130 border=0 x:str> <COLGROUP> <COL style="WIDTH: 20pt; mso-width-source: userset; mso-width-alt: 950" span=5 width=26> <TBODY> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 20pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" width=26 height=17>B</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 20pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right width=26 x:num>0</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 20pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right width=26 x:num>1</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 20pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right width=26 x:num>8</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 20pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right width=26 x:num>9</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>b</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>1</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>2</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>7</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>8</TD></TR></TBODY></TABLE>

Using the 1000's column and combining the possibilities that work give:

<TABLE style="WIDTH: 156pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=211 border=0 x:str> <COLGROUP> <COL style="WIDTH: 14pt; mso-width-source: userset; mso-width-alt: 694" span=3 width=19> <COL style="WIDTH: 14pt; mso-width-source: userset; mso-width-alt: 694" width=19> <COL style="WIDTH: 14pt; mso-width-source: userset; mso-width-alt: 694" span=6 width=19> <COL style="WIDTH: 16pt; mso-width-source: userset; mso-width-alt: 768" width=21> <TBODY> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" width=19 height=17>A</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>5</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>5</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 14pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=19 x:num>5</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 16pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" width=21 x:num>5</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl25 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>B</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>C</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>D</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>5</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>a</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>b</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num x:fmla="=+B1+B4">1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num x:fmla="=+C1+C4">2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num x:fmla="=+D1+D4">2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>c</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>0</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>d</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>1</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>2</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>6</TD> <TD class=xl24 style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" x:num>7</TD></TR></TBODY></TABLE>

Don't need to compare anymore because only one combination has 5 different digits. (plenty more comparisons are available but  50166107 works so no need to try and eliminate it).

p.s. you're right, I have nothing better to do.


  Posted by Rajal on 2004-08-11 17:47:28
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