mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

20 December

There are 6 different ways that three balls labelled 1 to 3 can be put into two boxes labelled A and B so that no box is empty:
How many ways can five balls labelled 1 to 5 be put into four boxes labelled A to D so that no box is empty?

Show answer

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?

17 December

If you expand \((a+b+c)^2\), you get \(a^2+b^2+c^2+2ab+2ac+2bc\). This has 6 terms.
How many terms does the expansion of \((a+b+c+d+e+f)^5\) have?

Show answer

16 December

Some numbers can be written as the sum of two or more consecutive positive integers, for example:
$$7=3+4$$ $$18=5+6+7$$
Some numbers (for example 4) cannot be written as the sum of two or more consecutive positive integers. What is the smallest three-digit number that cannot be written as the sum of two or more consecutive positive integers?

Show answer & extension

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

14 December

The function \(f(x)=ax+b\) (where \(a\) and \(b\) are real constants) satisfies
$$-x^3+2x^2+6x-9\leqslant f(x)\leqslant x^2-2x+3$$
whenever \(0\leqslant x\leqslant3\). What is \(f(200)\)?

Show answer

13 December

Today's number is given in this crossnumber. No number in the completed grid starts with 0.

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

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

Archive

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