{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Display","Solutions","Solutions 1-36"],"not_rendered":{"charts":1,"images":2,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Display","index":0,"n_rows":15,"n_cols":38,"rows_kept":15,"cut":false,"hidden":false,"merged":[[28,2,28,12],[0,3,0,31]]}
["N =",36,null,{"$f":"\"Circle of Perfect Squares – 1 to \"&B1","v":"Circle of Perfect Squares – 1 to 36"}]
[]
["Solution #  ",null,15,null,"Choose a solution from 1 to 31"]
[null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]
["Selected solution  ",null,1,8,17,32,4,12,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35,29,20,16,33,3,22,27,9,7,18,31,5,11,25,24]
["Adjacent sums",null,9,25,49,36,16,25,49,64,49,36,49,64,49,25,16,36,49,25,16,49,64,49,36,49,36,25,49,36,16,25,49,36,16,36,49,25]
["Square roots",null,{"$f":"SQRT(C6)","v":3},5,7,6,4,5,7,8,7,6,7,8,7,5,4,6,7,5,4,7,8,7,6,7,6,5,7,6,4,5,7,6,4,6,7,5]
[]
[]
[]
[]
[]
[]
[]
[null,null,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]

{"sheet":"Solutions","index":1,"n_rows":37,"n_cols":37,"rows_kept":37,"cut":false,"hidden":true,"merged":[]}
["Circle of Squares (1–36): distinct cycles (rotation+reversal reduced)"]
["Rotation fixed by starting at 1; reversal reduced by requiring 2nd < last."]
[]
["Total distinct solutions found:",31]
[]
[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]
[1,1,3,6,19,30,34,2,23,26,10,15,21,4,32,17,8,28,36,13,12,24,25,11,5,20,29,7,18,31,33,16,9,27,22,14,35]
[2,1,3,6,19,30,34,15,10,26,23,2,7,18,31,33,16,9,27,22,14,35,29,20,5,11,25,24,12,13,36,28,21,4,32,17,8]
[3,1,3,13,36,28,21,15,34,30,19,6,10,26,23,2,7,18,31,33,16,9,27,22,14,35,29,20,5,11,25,24,12,4,32,17,8]
[4,1,3,22,27,9,7,18,31,33,16,20,29,35,14,2,23,26,10,6,19,30,34,15,21,28,36,13,12,24,25,11,5,4,32,17,8]
[5,1,3,22,27,9,16,33,31,18,7,2,23,26,10,6,19,30,34,15,21,28,36,13,12,24,25,11,14,35,29,20,5,4,32,17,8]
[6,1,3,22,27,9,16,33,31,18,7,29,20,5,11,25,24,12,13,36,28,8,17,32,4,21,15,34,30,19,6,10,26,23,2,14,35]
[7,1,3,33,16,9,27,22,14,11,25,24,12,13,36,28,8,17,32,4,21,15,34,30,19,6,10,26,23,2,7,18,31,5,20,29,35]
[8,1,8,17,32,4,5,11,25,24,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,31,18,7,29,20,16,9,27,22,14,35]
[9,1,8,17,32,4,5,20,16,9,27,22,14,11,25,24,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,31,18,7,29,35]
[10,1,8,17,32,4,5,20,29,7,18,31,33,16,9,27,22,3,6,19,30,34,2,23,26,10,15,21,28,36,13,12,24,25,11,14,35]
[11,1,8,17,32,4,5,31,18,7,9,27,22,14,11,25,24,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,16,20,29,35]
[12,1,8,17,32,4,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,16,20,29,35,14,22,27,9,7,18,31,5,11,25,24]
[13,1,8,17,32,4,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,31,18,7,29,35,14,22,27,9,16,20,5,11,25,24]
[14,1,8,17,32,4,12,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35,29,7,18,31,33,3,22,27,9,16,20,5,11,25,24]
[15,1,8,17,32,4,12,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35,29,20,16,33,3,22,27,9,7,18,31,5,11,25,24]
[16,1,8,17,32,4,12,24,25,11,5,20,16,9,27,22,3,33,31,18,7,29,35,14,2,34,30,19,6,10,26,23,13,36,28,21,15]
[17,1,8,17,32,4,12,24,25,11,5,20,16,9,27,22,14,2,23,26,10,6,19,30,34,15,21,28,36,13,3,33,31,18,7,29,35]
[18,1,8,17,32,4,12,24,25,11,5,20,29,7,18,31,33,16,9,27,22,3,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35]
[19,1,8,17,32,4,12,24,25,11,5,31,18,7,9,27,22,3,33,16,20,29,35,14,2,34,30,19,6,10,26,23,13,36,28,21,15]
[20,1,8,17,32,4,12,24,25,11,5,31,18,7,9,27,22,14,2,23,26,10,6,19,30,34,15,21,28,36,13,3,33,16,20,29,35]
[21,1,8,17,32,4,12,24,25,11,14,22,27,9,16,33,3,13,36,28,21,15,34,30,19,6,10,26,23,2,7,18,31,5,20,29,35]
[22,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,16,9,27,22,3,33,31,18,7,29,35,14,2,23,26,10,6,19,30,34,15]
[23,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,16,9,27,22,14,2,23,26,10,15,34,30,19,6,3,33,31,18,7,29,35]
[24,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,16,9,27,22,14,35,29,7,18,31,33,3,6,19,30,34,2,23,26,10,15]
[25,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,29,7,18,31,33,16,9,27,22,3,6,19,30,34,15,10,26,23,2,14,35]
[26,1,8,17,32,4,21,28,36,13,12,24,25,11,5,31,18,7,9,27,22,3,33,16,20,29,35,14,2,23,26,10,6,19,30,34,15]
[27,1,8,17,32,4,21,28,36,13,12,24,25,11,5,31,18,7,9,27,22,14,2,23,26,10,15,34,30,19,6,3,33,16,20,29,35]
[28,1,8,17,32,4,21,28,36,13,12,24,25,11,5,31,18,7,9,27,22,14,35,29,20,16,33,3,6,19,30,34,2,23,26,10,15]
[29,1,8,17,32,4,21,28,36,13,12,24,25,11,14,22,27,9,16,33,3,6,19,30,34,15,10,26,23,2,7,18,31,5,20,29,35]
[30,1,8,28,36,13,12,24,25,11,5,20,16,9,27,22,14,35,29,7,18,31,33,3,6,10,26,23,2,34,30,19,17,32,4,21,15]
[31,1,8,28,36,13,12,24,25,11,5,31,18,7,9,27,22,14,35,29,20,16,33,3,6,10,26,23,2,34,30,19,17,32,4,21,15]

{"sheet":"Solutions 1-36","index":2,"n_rows":45,"n_cols":37,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
["Circle of Perfect Squares (1-36)"]
["Distinct cycles with rotation and reversal symmetry removed"]
["Starting value fixed at 1"]
["Maximum solutions to print",50]
["Stop after first solution",false]
["Status","Completed"]
["<-- Back to Summary"]
["Solution #",1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]
[1,1,3,6,19,30,34,2,23,26,10,15,21,4,32,17,8,28,36,13,12,24,25,11,5,20,29,7,18,31,33,16,9,27,22,14,35]
[2,1,3,6,19,30,34,15,10,26,23,2,7,18,31,33,16,9,27,22,14,35,29,20,5,11,25,24,12,13,36,28,21,4,32,17,8]
[3,1,3,13,36,28,21,15,34,30,19,6,10,26,23,2,7,18,31,33,16,9,27,22,14,35,29,20,5,11,25,24,12,4,32,17,8]
[4,1,3,22,27,9,7,18,31,33,16,20,29,35,14,2,23,26,10,6,19,30,34,15,21,28,36,13,12,24,25,11,5,4,32,17,8]
[5,1,3,22,27,9,16,33,31,18,7,2,23,26,10,6,19,30,34,15,21,28,36,13,12,24,25,11,14,35,29,20,5,4,32,17,8]
[6,1,3,22,27,9,16,33,31,18,7,29,20,5,11,25,24,12,13,36,28,8,17,32,4,21,15,34,30,19,6,10,26,23,2,14,35]
[7,1,3,33,16,9,27,22,14,11,25,24,12,13,36,28,8,17,32,4,21,15,34,30,19,6,10,26,23,2,7,18,31,5,20,29,35]
[8,1,8,17,32,4,5,11,25,24,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,31,18,7,29,20,16,9,27,22,14,35]
[9,1,8,17,32,4,5,20,16,9,27,22,14,11,25,24,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,31,18,7,29,35]
[10,1,8,17,32,4,5,20,29,7,18,31,33,16,9,27,22,3,6,19,30,34,2,23,26,10,15,21,28,36,13,12,24,25,11,14,35]
[11,1,8,17,32,4,5,31,18,7,9,27,22,14,11,25,24,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,16,20,29,35]
[12,1,8,17,32,4,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,16,20,29,35,14,22,27,9,7,18,31,5,11,25,24]
[13,1,8,17,32,4,12,13,36,28,21,15,10,26,23,2,34,30,19,6,3,33,31,18,7,29,35,14,22,27,9,16,20,5,11,25,24]
[14,1,8,17,32,4,12,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35,29,7,18,31,33,3,22,27,9,16,20,5,11,25,24]
[15,1,8,17,32,4,12,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35,29,20,16,33,3,22,27,9,7,18,31,5,11,25,24]
[16,1,8,17,32,4,12,24,25,11,5,20,16,9,27,22,3,33,31,18,7,29,35,14,2,34,30,19,6,10,26,23,13,36,28,21,15]
[17,1,8,17,32,4,12,24,25,11,5,20,16,9,27,22,14,2,23,26,10,6,19,30,34,15,21,28,36,13,3,33,31,18,7,29,35]
[18,1,8,17,32,4,12,24,25,11,5,20,29,7,18,31,33,16,9,27,22,3,13,36,28,21,15,34,30,19,6,10,26,23,2,14,35]
[19,1,8,17,32,4,12,24,25,11,5,31,18,7,9,27,22,3,33,16,20,29,35,14,2,34,30,19,6,10,26,23,13,36,28,21,15]
[20,1,8,17,32,4,12,24,25,11,5,31,18,7,9,27,22,14,2,23,26,10,6,19,30,34,15,21,28,36,13,3,33,16,20,29,35]
[21,1,8,17,32,4,12,24,25,11,14,22,27,9,16,33,3,13,36,28,21,15,34,30,19,6,10,26,23,2,7,18,31,5,20,29,35]
[22,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,16,9,27,22,3,33,31,18,7,29,35,14,2,23,26,10,6,19,30,34,15]
[23,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,16,9,27,22,14,2,23,26,10,15,34,30,19,6,3,33,31,18,7,29,35]
[24,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,16,9,27,22,14,35,29,7,18,31,33,3,6,19,30,34,2,23,26,10,15]
[25,1,8,17,32,4,21,28,36,13,12,24,25,11,5,20,29,7,18,31,33,16,9,27,22,3,6,19,30,34,15,10,26,23,2,14,35]
[26,1,8,17,32,4,21,28,36,13,12,24,25,11,5,31,18,7,9,27,22,3,33,16,20,29,35,14,2,23,26,10,6,19,30,34,15]
[27,1,8,17,32,4,21,28,36,13,12,24,25,11,5,31,18,7,9,27,22,14,2,23,26,10,15,34,30,19,6,3,33,16,20,29,35]
[28,1,8,17,32,4,21,28,36,13,12,24,25,11,5,31,18,7,9,27,22,14,35,29,20,16,33,3,6,19,30,34,2,23,26,10,15]
[29,1,8,17,32,4,21,28,36,13,12,24,25,11,14,22,27,9,16,33,3,6,19,30,34,15,10,26,23,2,7,18,31,5,20,29,35]
[30,1,8,28,36,13,12,24,25,11,5,20,16,9,27,22,14,35,29,7,18,31,33,3,6,10,26,23,2,34,30,19,17,32,4,21,15]
[31,1,8,28,36,13,12,24,25,11,5,31,18,7,9,27,22,14,35,29,20,16,33,3,6,10,26,23,2,34,30,19,17,32,4,21,15]
[]
["Total distinct solutions found:",31]
["Solutions printed:",31]
["Elapsed time (seconds):",1.63]
[]
["<-- Back to Summary"]