# generate all coloring configurations
# 0 = red, 1 = blue
configs = []
for i in range(512):
config = [(i & 1 << j) >> j for j in range(9)]
configs.append(config)
# find arithmetic sequence of length 3 in same color in each configuration
for c in configs:
found = False
for intv in range(1, 9):
if found:
break
for init in range(9):
length = 1
color = c[init]
for i in range(init+intv, 9, intv):
cur_color = c[i]
if cur_color != color:
break
length += 1
if length == 3:
found = True
break
print(f'an arithmetic sequence of length 3 in same color is {"not " if not found else ""}found for {c}')
