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March 5th, 2013, 05:40 AM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  fill in numbers in circles
[attachment=0:4ibmfuof]fill in the numbers in circles.jpg[/attachment:4ibmfuof]

March 5th, 2013, 07:39 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: fill in numbers in circles
4 four IV quatre Obvious that 13,14,15 are in top row. 
March 6th, 2013, 01:25 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: fill in numbers in circles
Hilite between lines to see triangle. ____________________________ [color=#E1EBF2]13 3 15 14 6 10 12 1 8 2 11 7 9 4 5[/color] _____________________________ @denis: 
March 6th, 2013, 06:26 AM  #4 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: fill in numbers in circles
Yes, a6=4. Now please fill in all the numbers in circles. 
March 6th, 2013, 06:50 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
If a6 = 4, a4 > 5 is impossible, as calculating the remaining integers requires an integer greater than 15. It follows that a4 = 5, making the rest of the numbers easy to calculate.

March 6th, 2013, 08:25 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: fill in numbers in circles
Or: since a6 = 4, then 13>a5>8 (due to 1,2,3 as givens and 13,14,15 in top row); then, with "2" above a5, then a5 can only be 9 or 10. Rest follows as per Skip. 

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