Weekly Problem 13 - 2013

2002 started on a Tuesday. In which years between now and 2015 will each date fall on the same day of the week as it fell that year?

Weekly Problem 46 - 2010

Consider a 10-digit number which contains only the numbers 1, 2 or 3. How many such numbers can you write so that every pair of adjacent digits differs by 1?

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

Weekly Problem 19 - 2015

An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?

Weekly Problem 15 - 2007

The Kings of Clubs, Diamonds, Hearts and Spades, and their respective Queens, are having an arm wrestling competition.

Weekly Problem 29 - 2015

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

Weekly Problem 4 - 2010

Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?

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

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?

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?

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?

Weekly Problem 24 - 2012

Can you put these very close fractions into order?

What is the last non-zero digit of $2^{57} \times 3^4 \times 5^{53}$?

Weekly Problem 44 - 2015

One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

Weekly Problem 35 - 2014

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?