mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.

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

Elastic numbers

Throughout this puzzle, expressions like \(AB\) will represent the digits of a number, not \(A\) multiplied by \(B\).
A two-digit number \(AB\) is called elastic if:
  1. \(A\) and \(B\) are both non-zero.
  2. The numbers \(A0B\), \(A00B\), \(A000B\), ... are all divisible by \(AB\).
There are three elastic numbers. Can you find them?

Show answer & extension

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

Fill in the digits

Source: Chalkdust
Can you place the digits 1 to 9 in the boxes so that the three digit numbers formed in the top, middle and bottom rows are multiples of 17, 25 and 9 (respectively); and the three digit numbers in the left, middle and right columns are multiples of 11, 16 and 12 (respectively)?

Show answer & extension

Always a multiple?

Source: nrich
Take a two digit number. Reverse the digits and add the result to your original number. Your answer is multiple of 11.
Prove that the answer will be a multiple of 11 for any starting number.
Will this work with three digit numbers? Four digit numbers? \(n\) digit numbers?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019