Everyday Maths
The mental arithmetic that saves you money in a shop, a showroom or a meeting.
A pseudo-random generator given the same starting value produces the same numbers forever. That is a feature and a limitation, and knowing which is which decides what you can use it for.
One die is even across all six faces. Two dice are a triangle peaking at 7, and 7 comes up six times as often as 2. Here is every outcome, counted.
Two machines that have never spoken can each invent an identifier and be confident they do not clash. The confidence comes from arithmetic, and the honest word is negligible — not zero.
The obvious way to shuffle a list is subtly wrong, and you can prove it by counting. Here are all 27 outcomes for a three-name list, and what the correct version changes.
One skewed set can have an average of 17.78 and an average of 5 at the same time, both correct. Here is how to tell which one you have been handed.
Two group averages of 80 and 50 do not make 65 if the groups are different sizes. Here is the worked example where the two methods disagree by nine points.
It is roughly the typical distance from the mean. Here is how to compute one by hand, why there are two divisors, and why the number means nothing on its own.
One line of algebra turns your current standing and the final's weight into the score you need. And if that score comes out above 100, the honest answer is to say so.