Patterns and Sequences Short Problems
Pattern Snake
This pattern repeats every 12 dots. Can you work out what a later piece will be?
What a Coincidence!
Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?
Suit Sequence
A pattern repeats every six symbols. What are the 100th and 101st symbols?
Knights and Knaves
Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?
Doubly Consecutive Sums
How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?
Expanding Pattern
How many squares are needed to continue this pattern?
Fibonacci Deduction
Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?
Hexagon Line
How many hexagons are required for the perimeter of the whole shape to have length 1002cm?
Street Lamps
Walking up a steep hill, I pass 10 equally spaced street lamps. How long do I take to walk from the first lamp to the last?
Fruit Line-up
This grocer wants to arrange his fruit in a particular order, can you help him?
Triangular Clock
Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?
Printing Error
Every third page number in this book has been omitted. Can you work out what number will be on the last page?
Sliding Robot
A robot moves along the number line. Where will it be after 2011 slides?
How Many Rectangles?
By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?
Night Watchmen
Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?
Knockdown
Weekly Problem 51 - 2016
Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?
Collatz 13
If a number is even, halve it; if odd, treble it and add 1. If a sequence starts at 13, what will be the value of the 2008th term?
12345
Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?
Collatz-ish
A sequence is generated using these rules. For which values of n is the nth term equal to n?
Below 400
Can you work out which number will appear directly below 400 in this pattern?
Trolley Park
In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?
Alternating Sum
Given that the number 2008 is the correct answer to a sum, can you find n?
Newspaper Sheets
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?