mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

24 December

There are six 3-digit numbers with the property that the sum of their digits is equal to the product of their digits. Today's number is the largest of these numbers.

Show answer

6 December

Noel's grandchildren were in born in November in consecutive years. Each year for Christmas, Noel gives each of his grandchildren their age in pounds.
Last year, Noel gave his grandchildren a total of £208. How much will he give them in total this year?

Show answer

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

Square pairs

Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

Show answer

14 December

In July, I posted the Combining Multiples puzzle.
Today's number is the largest number that cannot be written in the form \(27a+17b\), where \(a\) and \(b\) are positive integers (or 0).

Combining multiples

In each of these questions, positive integers should be taken to include 0.
1. What is the largest number that cannot be written in the form \(3a+5b\), where \(a\) and \(b\) are positive integers?
2. What is the largest number that cannot be written in the form \(3a+7b\), where \(a\) and \(b\) are positive integers?
3. What is the largest number that cannot be written in the form \(10a+11b\), where \(a\) and \(b\) are positive integers?
4. Given \(n\) and \(m\), what is the largest number that cannot be written in the form \(na+mb\), where \(a\) and \(b\) are positive integers?

Show answer & extension

Subsum

1) In a set of three integers, will there always be two integers whose sum is even?
2) How many integers must there be in a set so that there will always be three integers in the set whose sum is a multiple of 3?
3) How many integers must there be in a set so that there will always be four integers in the set whose sum is even?
4) How many integers must there be in a set so that there will always be three integers in the set whose sum is even?

Show answer & extension

Santa

Each of the letters D, A, Y, S, N, T, B, R and E represents a different non-zero digit. The following sum is true:
$$ \begin{array}{cccccc} D&A&D&D&Y\\ B&E&A&R&D&+\\ \hline S&A&N&T&A \end{array} $$
This has a unique solution, but I haven't found a way to find the solution without brute force. This less insightful sum is also true with the same values of the letters (and should allow you to find the values of the letters using logic alone):
$$ \begin{array}{ccccc} R&A&T&S\\ N&E&R&D&+\\ \hline S&A&N&E \end{array} $$

Show answer

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020