document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171228>Question 1171228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm really stuck, please help? Thanks! Here's the question\r<BR>\n" );
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document.write( "A prime number is an integer greater than 1 with exactly two different positive factors, 1 and the number itself. There are three children in a family. Each of their ages is a prime number. The sum of their ages is 41 and at least two of the children have ages that differ by 16. Determine all possibilities for the ages of the children. </SPAN>\n" );
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document.write( "There is nothing you can learn from having us work the problem for you.  There is no algebraic method for finding the different possibilities; you just need to try different combinations in an orderly way.<br><BR>\n" );
document.write( "The sum of the ages, 41, is an odd number; you can get an odd sum with three numbers either if two are even and one is odd, or if all three are odd.  Since there is only one even prime number, the only possibilities are with three odd ages.<br><BR>\n" );
document.write( "So search for them in an orderly way, by starting with the smallest possible age for the youngest.<br><BR>\n" );
document.write( "I'll get you started and let you have the satisfaction of finding the answers yourself.<br><BR>\n" );
document.write( "Suppose the youngest child's age is the smallest odd prime number, 3.  Then the sum of the other two ages must be 38.  Try the possibilities:<BR>\n" );
document.write( "3+3+35 no; 35 is not prime<BR>\n" );
document.write( "3+5+33 no; 33 is not prime<BR>\n" );
document.write( "etc....<br><BR>\n" );
document.write( "There may or may not be solutions with 3 as the age of the youngest.  So next try 5 for the age of the youngest, meaning the sum of the other two ages is 36:<BR>\n" );
document.write( "5+5+31 That is three prime numbers; but it doesn't satisfy the condition that two of the ages differ by 16.<BR>\n" );
document.write( "5+7+29 Likewise....<BR>\n" );
document.write( "5+11+25 no; 25 is not prime.<BR>\n" );
document.write( "etc....<br><BR>\n" );
document.write( "And after trying 5 as the age of the youngest, next try 7, then 11, ....<br><BR>\n" );
document.write( "The requirement that two of the ages differ by 16 will mean you won't have very many combinations to look at to find the ones that satisfy all the conditions.<br><BR>\n" );
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document.write( "Here is another approach to the problem that is probably faster than what is described above:<br><BR>\n" );
document.write( "Start by looking for pairs of relatively small prime numbers whose difference is 16.  There are probably very few such pairs, leading to a faster solution to the whole problem.<br><BR>\n" );
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