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Why does a tiny number rule resist a simple proof?

Start with a positive whole number. Halve it if it is even, or triple it and add one if it is odd: a rule simple enough to follow by hand leads to a surprisingly difficult question about every possible starting number.

5–7 min

Questions you could explore

  • Why can checking billions of examples still fall short of a proof?
  • What does a result about almost all starting values leave unsettled?

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Maths and statistics

When one long wait changes the average

An average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

5–7 min

When one long wait changes the average

Maths and statistics5–7 minAn average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

Maths and statistics

How is random sampling different from random assignment?

A study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

3–5 min

How is random sampling different from random assignment?

Maths and statistics3–5 minA study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

Why does the Gregorian calendar sometimes skip a leap year?

Maths and statistics2–3 minThe familiar 'every four years' rule has exceptions. The Gregorian calendar treated 1900 and 2000 differently because its century rules refine how calendar years track the solar year.

Why does a tiny number rule resist a simple proof? | Speech Topic | speaking.app