mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.

Show answer

13 December

There is a row of 1000 lockers numbered from 1 to 1000. Locker 1 is closed and locked and the rest are open.
A queue of people each do the following (until all the lockers are closed):
Today's number is the number of lockers that are locked at the end of the process.
Note: closed and locked are different states.

Show answer

7 December

There is a row of 1000 closed lockers numbered from 1 to 1000 (inclusive). Near the lockers, there is a bucket containing the numbers 1 to 1000 (inclusive) written on scraps of paper.
1000 people then each do the following:
Today's number is the number of lockers that will be closed at the end of this process.

Show answer

6 December

This puzzle was part of the 2018 Advent calendar.
This puzzle is inspired by a puzzle that Daniel Griller showed me.
Write down the numbers from 12 to 22 (including 12 and 22). Under each number, write down its largest odd factor*.
Today's number is the sum of all these odd factors.
* If a number is odd, then its largest odd factor is the number itself.

Show answer

Digitless factor

Ted thinks of a three-digit number. He removes one of its digits to make a two-digit number.
Ted notices that his three-digit number is exactly 37 times his two-digit number. What was Ted's three-digit number?

Show answer & extension

24 December

Today's number is the smallest number with exactly 28 factors (including 1 and the number itself as factors).

Show answer

21 December

The factors of 6 (excluding 6 itself) are 1, 2 and 3. \(1+2+3=6\), so 6 is a perfect number.
Today's number is the only three digit perfect number.

20 December

What is the largest number that cannot be written in the form \(10a+27b\), where \(a\) and \(b\) are nonnegative integers (ie \(a\) and \(b\) can be 0, 1, 2, 3, ...)?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024