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#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

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

Write the numbers 1, 2, 3, ... in a row. Strike out every third number beginning with the third. Write down the cumulative sums of what remains:

1, 2, 3, 4, 5, 6, 7, ...

1, 2, ~~3~~, 4, 5, ~~6~~, 7, ...

1, 2, 4, 5, 7, ...

1=1; 1+2=3; 1+2+4=7; 1+2+4+5=12; 1+2+4+5+7=19; ...

1, 3, 7, 12, 19, ...

Now strike out every second number beginning with the second. Write down the cumulative sums of what remains. What is the final sequence? Why do you get this sequence?

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

puzzles about numbers, or a random puzzle.

puzzles about numbers, or a random puzzle.