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.

Royal Arm Wrestling

Age 11 to 14 Short Challenge Level:

How many arm-wrestles will there be in the royal arm wrestling championship?

Suit Sequence

Age 11 to 14 Short Challenge Level:

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

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?

Halloween Day

Age 11 to 14 Short Challenge Level:

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

How Many Rectangles?

Age 11 to 14 Short Challenge Level:

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?

Take a Leaf

Age 11 to 14 Short Challenge Level:

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?

Almost Constant Digits

Age 11 to 14 Short Challenge Level:

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Not a Zero

Age 11 to 14 Short Challenge Level:

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

Too Close to Call

Age 11 to 14 Short Challenge Level:

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

Back in Time

Age 14 to 16 Short Challenge Level:

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

Newspaper Sheets

Age 14 to 16 Short Challenge Level:

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

Collatz-ish

Age 14 to 16 Short Challenge Level:

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

12345

Age 14 to 16 Short Challenge Level:

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