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logic square roots circles sum to infinity spheres squares grids coordinates cryptic clues remainders scales folding tube maps palindromes perfect numbers hexagons shapes cards partitions prime numbers arrows symmetry volume number triangles shape 2d shapes dodecagons routes addition bases crosswords indices division books integration calculus complex numbers percentages numbers 3d shapes lines rugby sums odd numbers speed trigonometry mean balancing wordplay star numbers probability area multiples sport chalkdust crossnumber factorials geometry doubling chess games digits coins ellipses surds integers clocks money algebra differentiation advent fractions quadratics pascal's triangle colouring ave menace means factors averages triangle numbers cube numbers chocolate irreducible numbers unit fractions proportion floors perimeter parabolas graphs multiplication polygons time taxicab geometry regular shapes cryptic crossnumbers rectangles dice functions sequences square numbers people maths angles christmas crossnumbers dates planes probabilty## Three digit numbers

Source: UKMT Pink Kangaroo 2012

Brigette wrote down a list of all 3-digit numbers. For each of the numbers on her list she found the product of the digits. She then added up all of these products. Which of the following is equal to her total?

**A**\(45\)

**B**\(45^2\)

**C**\(45^3\)

**D**\(2^{45}\)

**E**\(3^{45}\)

If you enjoyed this puzzle, check out Sunday Afternoon Maths X,

puzzles about numbers, or a random puzzle.

puzzles about numbers, or a random puzzle.