Puzzles
17 December
A sequence of zeros and ones can be reduced by writing a 0 or 1 under each pair of numbers: 1 is written if the numbers are the same, 0 is written if they are not.
This process can be repeated until there is a single number. For example, if we start with the sequence 1, 1, 1, 0, 1 (of length 5), we get:
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
The final digit is a 1.
How many sequences of zeros and ones of length 10 are there that when reduced lead to the final digit being a 1?
Archive
Show me a random puzzle Most recent collections
Advent calendar 2025
Advent calendar 2024
Advent calendar 2023
Advent calendar 2022
List of all puzzles
Tags
angles sport routes medians planes quadrilaterals unit fractions cryptic crossnumbers expansions time dates addition division dice menace proportion shape multiplication perimeter colouring graphs cards floors chocolate polynomials numbers books christmas multiplaction squares differentiation clocks geometric means lines calculus complex numbers scales coins mean speed volume combinatorics pentagons determinants partitions pascal's triangle quadratics wordplay geometry sums 2d shapes ave sequences shapes prime factors circles grids coordinates arrows triangle numbers crosswords parabolas digits area percentages palindromes matrices balancing spheres means tangents remainders symmetry powers crossnumbers doubling chalkdust crossnumber square numbers prime numbers logic probabilty square roots bases functions algebra polygons consecutive numbers the only crossnumber tiling elections dodecagons squares probability money lists axes cryptic clues decahedra hexagons binary digital clocks neighbours median integration dominos factorials xor taxicab geometry ellipses odd numbers factors products people maths star numbers perfect numbers albgebra number consecutive integers sets digital products cubics games sum to infinity fractions geometric mean indices folding tube maps rectangles surds even numbers averages irreducible numbers trigonometry square grids cube numbers multiples integers triangles tournaments chess gerrymandering range regular shapes advent 3d shapes rugby© Matthew Scroggs 2012–2026