6.
The first day of a new century can never be Sunday, Wednesday, or Friday. The cycle of the Gregorian calendar is completed in 400 years, after which all dates repeat themselves.
As in this cycle there are only four first days of a century, it is clear that three of the seven days of the week must be excluded. Any perpetual calendar shows that the four which do occur are Monday, Tuesday, Thursday, and Saturday, so that Sunday, Wednesday, and Friday are shut out.
A neat corollary to this proof is that Monday is the only day which may be the first, or which may be the last, day of a century.
7.
A cricket bat with spliced handle has such good driving power, because the elasticity of the handle allows the ball to be in contact with the blade of the bat for a longer time than would otherwise be possible.
With similar effect the “follow through” of the club head at golf maintains contact with the ball, when it is already travelling fast.