A Spiral of Numbers

★ 7/10combinatorics Arithmetic Progression Counting

Problem

Arrange $1, 2, \dots, n^2$ clockwise in a spiral to fill an $n \times n$ table $T_n$ , first row $1, 2, \dots, n$ ; for example

T_3 = \begin{bmatrix} 1&2&3 \\ 8&9&4 \\ 7&6&5 \end{bmatrix}.

In $T_{100}$ , the number $2018$ sits in row $i$ , column $j$ . Find $(i, j)$ .

Answer

Solution

Difficulty	7/10
Topics	combinatorics, Arithmetic Progression, Counting

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