Challenge: sum of squares. Let's break 299

[Allen]

number of unique solutions found for each round (includes reversals):
(this is not exhaustive, just how many were left after 1 run)

Unique solutions found for len 15: 2
Unique solutions found for len 16: 2
Unique solutions found for len 17: 2
Unique solutions found for len 23: 6
Unique solutions found for len 25: 20
Unique solutions found for len 26: 24
Unique solutions found for len 27: 58
Unique solutions found for len 28: 56
Unique solutions found for len 29: 20
Unique solutions found for len 30: 22
Unique solutions found for len 31: 142
Unique solutions found for len 32: 124
Unique solutions found for len 33: 44
Unique solutions found for len 34: 40
Unique solutions found for len 35: 88
Unique solutions found for len 36: 40
Unique solutions found for len 37: 46
Unique solutions found for len 38: 28
Unique solutions found for len 39: 18
Unique solutions found for len 40: 18
Unique solutions found for len 41: 24
Unique solutions found for len 42: 20
Unique solutions found for len 43: 30
Unique solutions found for len 44: 6
Unique solutions found for len 45: 24
Unique solutions found for len 46: 6
Unique solutions found for len 47: 2
Unique solutions found for len 48: 4
Unique solutions found for len 49: 12
Unique solutions found for len 50: 22
Unique solutions found for len 51: 8
Unique solutions found for len 52: 8
Unique solutions found for len 53: 18
Unique solutions found for len 54: 4
Unique solutions found for len 57: 8
Unique solutions found for len 60: 4
Unique solutions found for len 61: 4
Unique solutions found for len 63: 20
Unique solutions found for len 64: 12
Unique solutions found for len 65: 4
Unique solutions found for len 66: 8
Unique solutions found for len 67: 4
Unique solutions found for len 69: 2
Unique solutions found for len 71: 6
Unique solutions found for len 72: 36
Unique solutions found for len 73: 24
Unique solutions found for len 74: 22
Unique solutions found for len 76: 8
Unique solutions found for len 78: 14
Unique solutions found for len 80: 16
Unique solutions found for len 84: 14
Unique solutions found for len 85: 18
Unique solutions found for len 86: 6
Unique solutions found for len 87: 10
Unique solutions found for len 88: 26
Unique solutions found for len 89: 40
Unique solutions found for len 90: 16
Unique solutions found for len 91: 2
Unique solutions found for len 92: 10
Unique solutions found for len 93: 10
Unique solutions found for len 96: 6
Unique solutions found for len 97: 18
Unique solutions found for len 98: 8