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# 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

### Suit Sequence

### Take a Leaf

### Out of Sync

### Halloween Day

### How Many Rectangles?

### Knockdown

### Too Close to Call

### Almost Constant Digits

### Back in Time

### Newspaper Sheets

### Collatz-ish

### 12345

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This is part of our collection of Short Problems.

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

Weekly Problem 24 - 2012

Can you put these very close fractions into order?

Age 11 to 14

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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