mscroggs.co.uk
mscroggs.co.uk
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.

subscribe

Puzzles

4 December

If \(n\) is 1, 2, 4, or 6 then \((n!-3)/(n-3)\) is an integer. The largest of these numbers is 6.
What is the largest possible value of \(n\) for which \((n!-123)/(n-123)\) is an integer?

Show answer

3 December

190 is the smallest multiple of 10 whose digits add up to 10.
What is the smallest multiple of 15 whose digits add up to 15?

2 December

Holly adds up the first six even numbers, then adds on half of the next even number. Her total is 49.
Next, Holly adds up the first \(n\) even numbers then adds on half of the next even number. This time, her total is 465124. What is \(n\)?

Show answer & extension

1 December

Each interior angle of a regular triangle is 60°.
Each interior angle of a different regular polygon is 178°. How many sides does this polygon have?

Show answer

Advent 2022 logic puzzle

It's nearly Christmas and something terrible has happened: an evil Christmas-hater has set three drones loose above Santa's stables. As long as the drones are flying around, Santa is unable to take off to deliver presents to children all over the world. You need to help Santa by destroying the drones so that he can deliver presents before Christmas is ruined for everyone.
Each of the three drones was programmed with four integers between 1 and 20 (inclusive): the first two of these are the drone's starting position; the last two give the drone's daily speed. The drones have divided the sky above Santa's stables into a 20 by 20 grid. On 1 December, the drones will be at their starting position. Each day, every drone will add the first number in their daily speed to their horizontal position, and the second number to their vertical position. If the drone's position in either direction becomes greater than 20, the drone will subtract 20 from their position in that direction. Midnight in Santa's special Advent timezone is at 5am GMT, and so the day will change and the drones will all move at 5am GMT. For example, if a drone's starting position was (1, 12) and its movement was (5, 7), then:
You need to calculate each drone's starting position and daily speed, then work out where the drone currently is so you can shoot it down.
You can attempt to shoot down the drones here.

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

23 December

How many numbers are there between 100 and 1000 that contain no 0, 1, 2, 3, or 4?

Show answer

22 December

Ivy makes a sequence by starting with the number 35, then repeatedly making the next term by reversing the digits of the current number and adding 6. The first few terms of this sequence are:
$$35$$ $$53+6 = 59$$ $$95+6 = 101$$
What is the first number in Ivy's sequence that is smaller than the previous term?

Show answer

Tags: numbers

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

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

Archive

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