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Network Trees

Explore some of the different types of network, and prove a result about network trees.

Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Symmetricality

Five equations and five unknowns. Is there an easy way to find the unknown values?

Continuing to Explore Four Consecutive Numbers

Age 14 to 16
Challenge Level

If the first number is $a$, can you write down the second number in terms of $a$?  How about the third and fourth numbers?

Can you find an expression for the sum of the four consecutive numbers in terms of the first one?

What do all the numbers of the form $2k$ (where $k$ is an integer) have in common?  What about numbers of the form $2k+1$?