#43 Consecutive sums
set by Katie Steckles
Consecutive numbers are ones that follow on from each other in order, like 2, 3, 4 and 5. We can create certain numbers by adding together runs of consecutive numbers, e.g. 1 + 2 + 3 = 6 or 14 + 15 = 29.
Can you write 14 as a sum of two or more consecutive positive numbers?
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Which numbers below 20 cannot be written in this way, and is there a pattern?
Solution next week
#42 Persistence
Solution
The persistence of 77 is 4 and its root is 8: 77â¢49â¢36â¢18â¢8.
The smallest number with persistence 1 is 10.
No two-digit number has a persistence greater than 4 (and 77 is the only two-digit number with a persistence of exactly 4).
Quick quiz #275
set by Bethan Ackerley
1 Aperiodic monotiles can sometimes be referred to by what name? (One they share with a prominent 20th-century physicist.)
2 What does the GPT in ChatGPT stand for?
3 Philosopher John Searle created which thought experiment regarding artificial intelligence?
4 Medicines that alter contractions of the muscles are described as what?
5 Astronaut Gus Grissom was killed in which mission?
Answers on page 55
Quick quiz #275
Answers
1 Einsteins, though this isn't through any connection to the work of Albert Einstein, rather it is a play on the German words for "one stone"
2 Generative pre-trained transformer
3 The Chinese Room
4 Inotropic
5 Apollo 1