The question you opened
Cutting the log into six pieces
Cutting a log into 3 pieces takes 6 seconds.
How many seconds to cut the same log into 6 pieces?
15 seconds
Three pieces need two cuts, so one cut takes 3 seconds. Six pieces need five cuts, and five times 3 is 15.
Cutting a log into three pieces takes six seconds. Cutting the same log into six pieces takes fifteen seconds, and almost everyone says twelve. The twelve comes from doubling. Twice as many pieces, twice as long. It sounds fair, and it fails because the saw makes cuts rather than pieces, and the number of cuts is always one fewer than the number of pieces. Work it through. To get three pieces you cut the log twice.
Two cuts in six seconds means each cut takes three seconds. To get six pieces you need five cuts. Five cuts at three seconds each is fifteen seconds. Draw a line and mark it. One cut gives two pieces. Two cuts give three. Three cuts give four. The gap of one never closes, and it is the reason the time does not scale the way the pieces do. This off by one shows up all over the place once you know to look for it.
Fence posts along a straight fence: ten panels need eleven posts. Stairs between floors: from the sixth floor to the first there are five flights, not six. Days between dates: from Monday to Friday there are four nights rather than five. Trees planted along a path, beads separated by knots, chimes of a clock. Same shape every time. The habit is to ask what is actually being counted and what is being timed. Here the pieces are counted and the cuts are timed.
They are different things, and one of them is always one fewer than the other. There is a version that trips people the other way. Cutting a ring shaped rope into six pieces takes six cuts, not five, because a circle has no ends. That is worth knowing before you argue too confidently about the rule. If you want to check the answer without any arithmetic, hold up a hand. Five fingers, four gaps between them. Fingers and gaps are never the same number.
Technique: Count the cuts, not the pieces