[XXXXXXXXX][XXXXXXXXXXXXXXXXXXXX][XXXXXXXXXXXXXXXXXXXXXXX]
[X][X][X] [XXXXXXXX][XXXXXXXX] [XXXXXXXX][XXXXXXXX][X]
[XX][XX] [XX][XX] [XX][XX] [XX][XX]
[[1][2][3]][[[4A][4B]][[5A][5B]]][[[6A][6B]][[7A][7B]][8]]
Music
meets
Abstract
Mathematics
27 July 2023
Zurab Janelidze
Bethany Robinson
Hans Roosenschoon
Gerhard Woithe
1. Let X be a barber
2. Suppose X shaves those and only those who do not shave themselves
3. Suppose X shaves himself
4. Then X does not shave himself
5. Contradiction
6. Therefore X does not shave himself
7. Then X shaves himself
8. Contradiction
9. X cannot shave those and only those who do not shave themselves
10. No barber can shave those and only those who do not shave themselves
[XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX][XX]
_[X][XXXXXXXXXXXXXXXXXXXXXXX][X]_____
_____[X][XXXXXXXXX][X][X][X]_________
_________[X][X][X]___________________
[[1][[2][[3][4][5]][6][7][8]][9]][10]
[
[1]
[ [2] [[3][4][5]] [6] [7] [8] ]
[9]
]
[10]
“Cricket” by Hans Roosenschoon
[
[[1][2][3]]
[[[4A][4B]][[5A][5B]]]
[[[6A][6B]][[7A][7B]][8]]
]
[XXXXXXXXX][XXXXXXXXXXXXXXXXXXXX][XXXXXXXXXXXXXXXXXXXXXXX]
_[X][X][X]__[XXXXXXXX][XXXXXXXX]__[XXXXXXXX][XXXXXXXX][X]_
_____________[XX][XX]__[XX][XX]____[XX][XX]__[XX][XX]_____
[[1][2][3]][[[4A][4B]][[5A][5B]]][[[6A][6B]][[7A][7B]][8]]
[XXXXXXXXX][XXXXXXXXXXXXXXXXXXXX][XXXXXXXXXXXXXXXXXXXXXXX]
_[X][X][X]__[XXXXXXXX][XXXXXXXX]__[XXXXXXXX][XXXXXXXX][X]_
_____________[XX][XX]__[XX][XX]____[XX][XX]__[XX][XX]_____
[[1][2][3]][[[4A][4B]][[5A][5B]]][[[6A][6B]][[7A][7B]][8]]
How many block diagrams are there per number of blocks?