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 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019