This is part of our collection of Short Problems.
You may also be interested in our longer problems on Exploring and Noticing.
![What Two ...?](/sites/default/files/styles/medium/public/thumbnails/content-99-05-penta5-icon.jpg?itok=q0VZGk-U)
![Royal Arm Wrestling](/sites/default/files/styles/medium/public/thumbnails/content-id-5021-icon.png?itok=SvdV8Uq7)
problem
Royal Arm Wrestling
How many arm-wrestles will there be in the royal arm wrestling championship?
![Suit Sequence](/sites/default/files/styles/medium/public/thumbnails/content-id-11683-icon.png?itok=m3wWmn1B)
![Take a Leaf](/sites/default/files/styles/medium/public/thumbnails/content-id-10167-icon.png?itok=eZKtWqY9)
problem
Take a Leaf
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?
![Halloween Day](/sites/default/files/styles/medium/public/thumbnails/content-id-10192-icon.png?itok=W408nDoW)
problem
Halloween Day
One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.
![How many Rectangles?](/sites/default/files/styles/medium/public/thumbnails/content-id-11658-icon.png?itok=MP4YOToB)
problem
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?
![Knockdown](/sites/default/files/styles/medium/public/thumbnails/content-id-11677-icon.png?itok=NQnSRDhY)
problem
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?
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?
![Out of Sync](/sites/default/files/styles/medium/public/thumbnails/content-id-2512-icon.jpg?itok=FE6v1ZUQ)
problem
Out of Sync
Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?
![Almost Constant Digits](/sites/default/files/styles/medium/public/thumbnails/content-id-7140-icon.png?itok=931cqtfw)
problem
Almost Constant Digits
How many 10-digit numbers containing only 1s, 2s and 3s can you write?
![Too Close to Call](/sites/default/files/styles/medium/public/thumbnails/content-id-2451-icon.png?itok=8Q3brEos)
problem
Too Close to Call
Weekly Problem 24 - 2012
Can you put these very close fractions into order?
Can you put these very close fractions into order?
![Newspaper Sheets](/sites/default/files/styles/medium/public/thumbnails/content-id-7180-icon.png?itok=V8tkG7FL)
problem
Newspaper Sheets
From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
![Collatz-ish](/sites/default/files/styles/medium/public/thumbnails/content-id-10131-icon.png?itok=gUrhxfxC)
problem
Collatz-ish
A sequence is generated using these rules. For which values of n is the nth term equal to n?
![Back in Time](/sites/default/files/styles/medium/public/thumbnails/content-id-10177-icon.png?itok=LB3xYGMr)
problem
Back in Time
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
![Oldest and Youngest](/sites/default/files/styles/medium/public/thumbnails/content-id-11702-icon.png?itok=Qva3cpsT)
problem
Oldest and Youngest
Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?
![12345](/sites/default/files/styles/medium/public/thumbnails/content-04-weekly-prob20-icon.png?itok=IoGo4sVR)
problem
12345
Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?
![Day of the Triffids](/sites/default/files/styles/medium/public/thumbnails/content-id-2833-icon.png?itok=bBmPpHtq)
problem
Day of the Triffids
Jasmine buys three different types of plant. How many triffids did she buy?