document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188708>Question 1188708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> four young children are seated next to each other  on a bench. The child on the left cannot be older than the child on the right. The ages of 1st and 3rd children differ by 8 years. No child is below 2 years old, neither any of them is older than 10 years old. Then 2nd child is 7 years younger than the 4th child .What are the ages of the four children? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819860 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will assume the \"child on the left\" is the first child and the one on the right is the fourth....<br><BR>\n" );
document.write( "Let's call them, left to right, A, B, C, and D:<br><BR>\n" );
document.write( "(A, B, C, D)<br><BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "(1) A is not older than D<BR>\n" );
document.write( "(2) The age difference between A and C is 8 years<BR>\n" );
document.write( "(3) The minimum and maximum ages are 2 and 10<BR>\n" );
document.write( "(4) B is 7 years younger than D<br><BR>\n" );
document.write( "From (2) and (3), the ages of A and C are either 2 and 10, or 10 and 2:<br><BR>\n" );
document.write( "(5) (2, B, 10, D) or (10, B, 2, D)<br><BR>\n" );
document.write( "From (4), the ages of B and D are either 2 and 9, or 3 and 10:<br><BR>\n" );
document.write( "(6) {A, 2, C, 9) or (A, 3, C, 10)<br><BR>\n" );
document.write( "Combining (5) and (6), we get four possibilities:<BR>\n" );
document.write( "(2, 2, 10, 9)<BR>\n" );
document.write( "(2, 3, 10, 10)<BR>\n" );
document.write( "(10, 2, 2, 9)<BR>\n" );
document.write( "(10, 3, 2, 10)<br><BR>\n" );
document.write( "Those four possibilities all satisfy given conditions (2), (3), and (4); we need to see which one(s) satisfy condition (1).<br><BR>\n" );
document.write( "A is older than D (so condition (1) is not satisfied) in only one of the four possibilities; so we see that three of the four possibilities we have satisfy (1):<br><BR>\n" );
document.write( "(2, 2, 10, 9)<BR>\n" );
document.write( "(2, 3, 10, 10)<BR>\n" );
document.write( "(10, 3, 2, 10)<br><BR>\n" );
document.write( "All three of these sets of ages satisfy all the conditions of the problem.  Since the statement of the problem suggests that there is a single solution, the problem is faulty.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );