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Advent calendar 2015

22 December

What is the largest number which cannot be written as the sum of distinct squares?

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combinatorics integers functions lines square grids sum to infinity wordplay probabilty scales powers graphs volume perimeter 3d shapes crossnumbers money sequences irreducible numbers pentagons doubling spheres coins range coordinates trigonometry cards chess geometric mean odd numbers quadrilaterals planes probability algebra menace number decahedra colouring parabolas books crosswords means multiplication multiplaction squares star numbers indices differentiation grids hexagons fractions time proportion matrices 2d shapes shapes regular shapes tiling complex numbers neighbours palindromes tangents elections folding tube maps cryptic clues chalkdust crossnumber division xor cube numbers perfect numbers clocks games remainders integration dice ave geometry binary pascal's triangle albgebra calculus lists shape determinants consecutive integers people maths multiples sums dominos arrows percentages symmetry geometric means mean addition sport polygons factors dodecagons axes median rectangles factorials chocolate tournaments numbers unit fractions christmas area sets prime numbers taxicab geometry angles advent expansions partitions circles even numbers dates medians surds triangle numbers cubics averages digits consecutive numbers logic digital products square numbers speed floors bases routes digital clocks polynomials square roots the only crossnumber products balancing prime factors cryptic crossnumbers rugby gerrymandering ellipses quadratics triangles squares

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