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135 = 11 + 32 + 53
135 has the special property that it is equal to the sum of the first digit to the power 1, the second digit to the power 2 and the third digit to the power 3.
There are another three 3-digit numbers that have this property. Find one of them.
A gardener makes a fish pond which has 12 equal sides and all the sides are at right angles to each other.
The perimeter of the pond (in m) is equal to the area of the pond.
What is the area of the pond?
A newspaper is made of 8 large sheets of paper folded in half.
The newspaper has 32 pages altogether.
The first sheet contains pages 1, 2, 31 and 32.
I pick up a sheet containing page 25.
What is the total of the page numbers on this sheet?
Squares with side lengths 3 cm and 2 cm overlap as shown.
What is the difference between the areas of the two yellow shaded parts of each square?
A farmer has 41 sheep.
His farm is surrounded by 8 fields.
There is a window in each side of the house from which he can see 3 fields.
How should the sheep be put in the fields so he can see exactly 15 sheep from each window?
Chris and Danny start at the same point.
They walk in opposite directions to each other for 3 metres,
then turn right and walk another 4 m.
How far apart are they now?
Noah watched 12 legs walk past him into the ark.
How many creatures could he have seen?
We want the complete range of possible answers.
A 10ticks book is published.
The pages are numbered 1, 2, 3…. etc.
When the page numbers where inspected it was noticed there were 555 digits used.
How many pages were in the book?
How many fives were used?
Which numbers, less than 100, are the product of exactly three different prime factors?
The electricity has gone out and Beth and Keith are getting dressed in the dark.
Beth has 6 yellow socks and 8 black socks in her drawer.
She wants two of the same colour.
How many will she have to take out to guarantee a matching pair?
Keith has 6 black socks, 8 blue socks and 4 green socks in his drawer.
He wants to wear socks that don’t match.
How many will he have to take out to guarantee that a pair that don’t match?