So the correct answer was five, and the binary made sense. I'm still really confused about the BT answer, though.
The BT answer has 5 slots, and I understand the decision you made to give each slot over to a character rather than necessarily a value. So the value "-1" takes two slots, even though it's a single value and in 'true BT" would just sit in its place value slot.
So, I feel like the answer the computer accepted 1-1-1, in true BT, would have been six, minus three, minus one.