You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

Calendar Capers

Choose any three by three square of dates on a calendar page...

problem icon

Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Newspaper Sheets

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

If page $1$ is on the outside of the first sheet, then page $2$ is on the inside. Pages $3$ and $4$ are on the same sheet, as are pages $5$ and $6$. This therefore shares a sheet with page $7$, so is the inside of the sheet.

On the outside on the other side is therefore page $62$. The other three sheets have pages $63$ and $64$, $65$ and $66$ and $67$ and $68$ on them. Therefore there are $68$ pages, and four sheets per page, so $17$ sheets.


Alternatively, the sum of the page numbers on the same side of the sheet is always constant, since one side increases by $1$ every time the other decreases by $1$. This means the total is always $8 + 61 = 69$, so page $1$ shares with page $68$. Hence there are $68$ pages, so $17$ sheets.


 

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem