mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

24 December

When written in binary, the number 235 is 11101011. This binary representation starts and ends with 1 and does not contain two 0s in a row.
What is the smallest three-digit number whose binary representation starts and ends with 1 and does not contain two 0s in a row?

Show answer

21 December

There are 6 two-digit numbers whose digits are all 1, 2, or 3 and whose second digit onwards are all less than or equal to the previous digit:
How many 20-digit numbers are there whose digits are all 1, 2, or 3 and whose second digit onwards are all less than or equal to the previous digit?

Show answer & extension

19 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the numbers in the red boxes.
+= 7
× × ×
+= 0
÷ ÷ ÷
+= 2
=
4
=
35
=
18

Show answer

Tags: numbers, grids

18 December

Some numbers can be written as the product of two or more consecutive integers, for example:
$$6=2\times3$$ $$840=4\times5\times6\times7$$
What is the smallest three-digit number that can be written as the product of two or more consecutive integers?

15 December

The arithmetic mean of a set of \(n\) numbers is computed by adding up all the numbers, then dividing the result by \(n\). The geometric mean of a set of \(n\) numbers is computed by multiplying all the numbers together, then taking the \(n\)th root of the result.
The arithmetic mean of the digits of the number 132 is \(\tfrac13(1+3+2)=2\). The geometric mean of the digits of the number 139 is \(\sqrt[3]{1\times3\times9}\)=3.
What is the smallest three-digit number whose first digit is 4 and for which the arithmetic and geometric means of its digits are both non-zero integers?

Show answer & extension

12 December

What is the smallest value of \(n\) such that
$$\frac{500!\times499!\times498!\times\dots\times1!}{n!}$$
is a square number?

Show answer

11 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the numbers in the red boxes.
++= 15
+ + ÷
+= 10
+ ×
÷×= 3
=
16
=
1
=
30

Show answer

Tags: numbers, grids

10 December

How many integers are there between 100 and 1000 whose digits add up to an even number?

Show answer

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

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

Archive

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