mscroggs.co.uk

mscroggs.co.uk

blog puzzles academic talks contact subscribe ↓ ☰ ↓

Advent calendar 2022

4 December

This puzzle was part of the 2022 Advent calendar.

All 2022 advent puzzles ~ More information

The last three digits of

5^{5}

are 125.

What are the last three digits of

5^{2, 022, 000, 000}

?

Show answer

Hide answer

The last three digits of

5^{1}

to

5^{7}

are:

\begin{aligned} 5^{1} & = 5 & \to & 5 \\ 5^{2} & = 25 & \to & 25 \\ 5^{3} & = 125 & \to & 125 \\ 5^{4} & = 625 & \to & 625 \\ 5^{5} & = 3125 & \to & 125 \\ 5^{6} & = 15625 & \to & 625 \\ 5^{7} & = 78125 & \to & 125 \end{aligned}

This pattern continues: the last three digits of 5 to the power of any odd number (greater than 2) is 125, and the last three digits of 5 to the power of any even number (greater than 3) is 625. The last three digits of

5^{2, 022, 000, 000}

are therefore 625.

Archive

Show me a random puzzle

Most recent collections

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼

© Matthew Scroggs 2012–2025