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Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Neighbours

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Page Numbers

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Fingers and Hands

Age 7 to 11 Challenge Level:


We had many solutions to the numerical questions we posed. From the United Kingdom: Louis, Lucy and Gabriel from Ickford, Taylor from Hillocks, Kieran from Gosforth, Shane and Sameer from Haberdashers, Rohan from Canon Lane.





Charlotte from Laurence Jackson school sent in the following straight-forward ideas that resemble the other solutions sent in.





Solution $1$: count the number of hands and times that number by $5$ which is the number of fingers and thumb on a person's hand.

Solution $2$: simply count the fingers in the picture.



Luke from High Wycombe Maths Master Class sent in,





There are $250$ hands altogether if you count in $5$s it makes it much easier. Hint: the first picture has $30$.



Katrina, Abigail and Aiden from St. Andrew's sent in the solutions clearly as:





Picture $1 - 30$ fingers

Picture $2 - 40$ fingers

Picture $3 - 50$ fingers

Picture $4 - 60$ fingers

Picture $5 - 70$ fingers

We thought the best way to count the fingers was to count the hands in $5$s. You could count pairs of hands in $10$s or count the number of hands and multiply them by $5$ to get the number of fingers.



From the United States of America, solutions were sent in from Conor at Burr Elementary School and Caroline from Estes Hills.





Thank you all for your answers and we welcome any later ones as well.

Did any of you try the last part of the problem, where the challenge was to count using aliens' hands? Do let us know if you've had a go.