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Product Four Times Sum (Posted on 2007-11-23)

Difficulty: 4 of 5

What are all the ordered triples of positive integers (x,y,z) with x<y<z, such that their product is four times their sum?

See The Solution Submitted by Charlie

Rating: 3.0000 (3 votes)

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Excel!

| Comment 1 of 5

An Excel + Macro solution which by exhaustive random analysis (range 0 to 1000) came up with the folowing solutions:

<TABLE style="WIDTH: 162pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=216 border=0 x:str> <COLGROUP> <COL style="WIDTH: 54pt" span=3 width=72> <TBODY> <TR style="HEIGHT: 14.25pt" height=19> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 54pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" align=right width=72 height=19 x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 54pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right width=72 x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 54pt; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right width=72 x:num>

</TD></TR> <TR style="HEIGHT: 14.25pt" height=19> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" align=right height=19 x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD></TR> <TR style="HEIGHT: 14.25pt" height=19> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" align=right height=19 x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD></TR> <TR style="HEIGHT: 14.25pt" height=19> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" align=right height=19 x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD></TR> <TR style="HEIGHT: 14.25pt" height=19> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent" align=right height=19 x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD> <TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; BORDER-BOTTOM: #d4d0c8; BACKGROUND-COLOR: transparent" align=right x:num>

</TD></TR></TBODY></TABLE>

Posted by Fernando on 2007-11-23 14:31:19

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