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.

Newspaper Sheets

KS 2 & 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 29 - 2011
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

Out of Sync

KS 2 & 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 15 - 2013
Albert Einstein could see two clocks. One changed 10 seconds early, the other changed 10 seconds late. For what fraction of the day did they show the same time?

Stuck in the Past

KS 2 & 3 Short Challenge Level:

Challenge Level:1

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?

Suit Sequence

KS 3 Short Challenge Level:

Challenge Level:1

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

Take a Leaf

KS 3 Short Challenge Level:

Challenge Level:1

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

KS 3 Short Challenge Level:

Challenge Level:1

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

KS 3 Short Challenge Level:

Challenge Level:1

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 Lies

KS 3 Short Challenge Level:

Challenge Level:1

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

12345

KS 3 Short Challenge Level:

Challenge Level:1

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

KS 3 Short Challenge Level:

Challenge Level:1

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?

Knockdown

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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 Rectangles?

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Too Close to Call

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Halloween Day

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

KS 4 Short Challenge Level:

Challenge Level:1

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

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Odd One Out

KS 5 Short Challenge Level:

Challenge Level:1

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