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#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

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#### Sunday Afternoon Maths LXVI

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

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

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

**Posted on 2014-08-17**

## 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?

## Whist

Messrs. Banker, Dentist, Apothecary and Scrivener played whist last night. (whist is a four player card game where partners sit opposite each other.) Each of these gentlemen is the namesake of another's vocation.

Last night, the apothecary partnered Mr. Apothecary; Mr. Banker's partner was the scrivener; on Mr. Scrivener's right sat the dentist.

Who sat on the banker's left?

If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVII,

puzzles about hexagons, or a random puzzle.

puzzles about hexagons, or a random puzzle.