# Puzzles

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