#34 Square dealing
set by Phil Lloyd
If a2 + b2 = c2, and a, b and c are three consecutive positive integers, what is the value of a? (You may know an example of a famous theorem that fits here.)
If d2 + e2 + f2 = g2 + h2, where d, e, f, g and h are five consecutive positive integers, what is the value of d?
After that, the next two sequences in this family have seven and nine consecutive positive integers. They start with 21 and 36. What do you notice about the starting numbers?
The next sequence after that will use 11 numbers. What is the first one?
Solution next week
#33 Number triangles
Solution
The completed triangles are:
The other ways to fill a triangle with the numbers 1-10 are:
Quick quiz #266
set by Bethan Ackerley
1 In botany, seed pods that remain closed at maturity are known as what?
2 In what year was the US space station Skylab deorbited?
3 Herring bodies in the posterior pituitary gland store oxytocin or which other hormone?
4 What is the taxonomic rank between kingdom and class?
5 Knap of Howar and Skara Brae are Neolithic sites on which island group?
Quick quiz #266
Answers
1 Indehiscent
2 1979
3 Antidiuretic hormone
4 Phylum
5 Orkney, off the coast of mainland Scotland
Article amended on 28 August 2024
Orkney is off the coast of mainland Scotland