mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

20 December

p(x) is a polynomial with integer coefficients such that:
What is p(23)?

Show answer

24 December

The expression \((3x-1)^2\) can be expanded to give \(9x^2-6x+1\). The sum of the coefficients in this expansion is \(9-6+1=4\).
What is the sum of the coefficients in the expansion of \((3x-1)^7\)?

Show answer

8 December

The equation \(x^5 - 7x^4 - 27x^3 + 175x^2 + 218x = 840\) has five real solutions. What is the product of all these solutions?

Show answer & extension

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

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025