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Author  Topic

TchrWill

USA
79 Posts

 Posted - 04/19/2013 :  14:13:51 Determine the location of the integers 1 through 12 in the circles so that the sum of the numbers in each of the six rows is the same? Is there more than one solution?.............O.......O..O..O..O.........O.....O.......O..O..O..O.............O Edited by - TchrWill on 04/19/2013 14:19:19

the_hill1962

USA
1468 Posts

 Posted - 04/20/2013 :  23:14:37 I only see 5 rows.There must be something that I am not seeing correctly because, as I see it, there is no solution. The 1st and 5th row only have one circle in each. The sum could not be the same because different integers would be put in them.Maybe the rows are verticle? However, I see seven 'columns' of circles. Edited by - the_hill1962 on 04/20/2013 23:20:42

someguy

143 Posts

 Posted - 04/21/2013 :  04:37:42 the_hill, I see it as a 6 pointed start made up of two triangles.The edges of the triangles are the six 'rows'.Each row has 4 numbers and each number is in two rows.The 4 numbers in each row must all sum to the same value.Although I had not seen this one before, I have seen a similar buteasier problem (figuring out how to create a 3 by 3 magic squarewithout guessing or using the 'pattern' to fill in the numbers).The same technique works here.The first step is to figure out what each row sums to.Good luck (there is more than one solution).

TchrWill

USA
79 Posts

Ultraglide

299 Posts

 Posted - 04/21/2013 :  12:52:39 Here's a hint: Each circle appears in exactly two lines so each number is used twice.

Ultraglide

299 Posts

 Posted - 04/22/2013 :  17:20:28 You beat me to it, that was my next hint: the lines have to add up to 26. There are more than 6 groupings that add up to 26 so this is more difficult than the 3x3 magic square where there is only one solution (sum 15) - all other solutions are rotations or reflections of the same square.

TchrWill

USA
79 Posts