mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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
If you enjoyed this puzzle, check out Sunday Afternoon Maths XXV,
puzzles about numbers, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021