Exploring and Noticing Structure - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Exploring and Noticing Structure.

Stuck in the Past

Age 7 to 14 Short Challenge Level:

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 Lies

Age 11 to 14 Short Challenge Level:

Weekly Problem 4 - 2010
Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?

12345

Age 11 to 14 Short Challenge Level:

Weekly Problem 50 - 2011
Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

Almost Constant Digits

Age 11 to 14 Short Challenge Level:

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?

Suit Sequence

Age 11 to 14 Short Challenge Level:

Weekly Problem 8 - 2017
A pattern repeats every six symbols. What are the 100th and 101st symbols?

Take a Leaf

Age 11 to 14 Short Challenge Level:

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?

Royal Arm Wrestling

Age 11 to 14 Short Challenge Level:

Weekly Problem 15 - 2007
The Kings of Clubs, Diamonds, Hearts and Spades, and their respective Queens, are having an arm wrestling competition.

Back in Time

Age 11 to 14 Short Challenge Level:

Weekly Problem 29 - 2015
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

How Many Rectangles?

Age 11 to 14 Short Challenge Level:

Weekly Problem 37 - 2016
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?

Knockdown

Age 11 to 14 Short Challenge Level:

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?

Newspaper Sheets

Age 11 to 14 Short Challenge Level:

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

Out of Sync

Age 11 to 14 Short Challenge Level:

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

Too Close to Call

Age 11 to 14 Short Challenge Level:

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

Halloween Day

Age 11 to 16 Short Challenge Level:

Weekly Problem 44 - 2015
One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

Collatz-ish

Age 14 to 16 Short Challenge Level:

Weekly Problem 35 - 2014
A sequence is generated using these rules. For which values of n is the nth term equal to n?

Not a Zero

Age 14 to 16 Short Challenge Level:

Weekly Problem 45 - 2017
What is the last non-zero digit of $2^{57} \times 3^4 \times 5^{53}$?

Odd One Out

Age 16 to 18 Short Challenge Level:

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