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UKMT Junior Mathematical Challenge, 2016

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows the first few squares of a 'spiral' sequence of squares. All but the first three squares have been numbered. After the first six squares, the sequence is continued by placing the next square alongside three existing squares – the largest existing square and two others. The three smallest squares have sides of length 1. What is the side length of the 12th square?

(A) $153$ (B) $123$ (C) $83$ (D) $53$ (E) $13$

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