A chunk is named after the number of squares it contains, or sometimes by its shape. For example, all the dark grey chunks are called 4-chunks and one of them is a 2 by 2 chunk.

The value of a chunk is the sum of the numbers on its squares. For example, the light grey 9-chunk has value (57+58+59+60+69+70+78+79+88=618).

A chunk must be in one piece. It cannot have parts joined at a corner, for example 71,72,83,84. It must not have holes, for example 71,72,73,81,83,91,92,93.

a) On a blank 100-chart, shade in a chunk that has value 600 and the fewest squares. Explain why there is no chunk of value 600 with fewer squares.

b) Explain why every rectangular 15-chunk has a value divisible by 15.

c) Explain why no rectangular 16-chunk has a value divisible by 16.

d) The square 9-chunk [5, 6, 7, 15, 16, 17, 25, 26, 27] has the unusual property that its value 144 is itself a square number. Find the two largest square chunks that have a square value.