2 out of 3
If it takes 852 digits to number all the pages of a book, what is the number of the last page?
2 out of 3
What is the largest number Sophie can use to have seven positive integers with a mean of 7?
2 out of 3
If Clara spends £23 on books and magazines, how many of each does she buy?
2 out of 3
Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?
2 out of 3
Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?
3 out of 3
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
3 out of 3
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
3 out of 3
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.
3 out of 3
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
3 out of 3
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
