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?

Show answer & extension

Tags: numbers


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?

Show answer & extension

Tags: logic, cards
If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about addition, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020