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Morgan's Work

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I started by ordering the numbers in consecutive/ sequential order across each row. 1 was in the top left-hand box and 9 was in the bottom right-hand box. Similar to below..

1 2 3

4 5 6

7 8 9

Then, I found the sum for each circle based on this arrangement. Next, I will do the same process except order the numbers in sequential down each column. Similar to below...

1 4 7

2 5 8

3 6 9

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Begin with filling in the possibilities for the white squares (listing them inside the white square to keep track of those possibilities, then do the same for the dark pink squares to see if I come upon a square in which it clear that only 1 of those possibilities will work.

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After staring at the puzzle for a while I realized that if the 3 dark pink squares add up to 16, the light pink square in the middle has to be 3. I think I will label each square a,b,c,d… so that would make e=3. I hope knowing this will help knock out other squares.

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I first noticed without really trying that 15 would be made by 2 digits, so I thought either 9+6 or 7+8. I wrote out the digits 123456789 so I can cross them out when I am done using them. Then…When you pointed out that the 4 boxes around the 19 would be what add up to 19, that is when I noticed that the middle box must be 3 (the dark pink 3 boxes add up to 16, so 19-16=3).  So my plan going forward is to keep looking for what I know.

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i immediately started writing all possible sum combos for every group of squares. I thought, if I factor in all of the combinations, I would be able to find at least one square and that would unlock the rest.

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I labeled the boxes alphabetically starting from the top left down to the bottom right.

A.  B.  C.

D.  E.  F.

G.  H.  I.

Then I set it up as a set of equations:

A+D+E+G = 14

B + C + F = 16

H + I = 15

A + B + D + E = 16

B + C + E + F = 19

E + F + H + I = 23

D + E + G + H = 22

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my first thought is to figure out the white squares because there are only two of them and they have to add up to 15. That seems like the easiest way to start the puzzle.

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My plan for the puzzle is to start with the white boxes and work upwards and out.  My reasoning is that I think there are fewer possible solutions to x+y = z than there are to a+b+c=d.  I know that the bottom numbers are more likely to be higher in value because the squares of 4 add up to numbers in the 20s as opposed to the teens.  So I figure I'll get the higher numbers  solved first and then be left with smaller numbers to arrange toward the top.

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I attacked this puzzle like a sudoku. like Katherine, I figured out 3 must go in the middle, then since the white squares were 15 + 3 = 18 the right middle square had to be 5. After that, I played around a bit with the numbers knowing that 8 and 9 were most likely surrounding the highest sums. A little strategy, a little guess and check. - Ben