Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

How many squares are needed to continue this pattern?

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?

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

A pattern repeats every six symbols. What are the 100th and 101st symbols?

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?

This grocer wants to arrange his fruit in a particular order, can you help him?

Every third page number in this book has been omitted. Can you work out what number will be on the last page?

This pattern repeats every 12 dots. Can you work out what a later piece will be?

A robot moves along the number line. Where will it be after 2011 slides?

Can you work out what fraction of this grid is shaded?

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?

This tiled floor has 109 purple tiles. How many tiles are there altogether?

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?

How many hexagons are required for the perimeter of the whole shape to have length 1002cm?

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?

Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?

In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

Can you work out which number will appear directly below 400 in this pattern?

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?

A sequence is generated using these rules. For which values of n is the nth term equal to n?

Given that the number 2008 is the correct answer to a sum, can you find n?

How many diagonals does a regular icosagon (20 sides) have?