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Let's define a new type of triangle called Lacsap's triangle, in which we put 1's down the left outside diagonal, pick entries for the right outside diagonal, and then subtract entries, from right to left, in each row to get the entries in the row below. For example, if we start with:

 



we can construct Lacsap's triangle from this starting position, and we get

 


(For example, 4=5-1, 3=4-1, -2=2-4, and so on. We leave the lower-right corner blank.)

If we start with:

 



what do we get as our final row (the four entries marked with blanks)? Enter your answer as an ordered list of four numbers (leaving the lower-right corner blank). For example, in our first triangle above, you would have entered (1,2,-5,9).

 May 10, 2016
 #1
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-3

1,3,10,7

 May 10, 2016
 #2
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                                                        1

                                               1              6

                                          1           5           12

                                      1        4             7           8  

                                        3          3           1

 

( 1, 3, 3, 1 )

 

 

 

cool cool cool

 May 10, 2016

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