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"Lower Secondary"
Suppose you had the never ending task of writing out all the natural numbers: 1, 2, 3, 4, 5…. and so on.
What would be the 1000th digit you would write down?
In what number would it occur?
What number would contain the millionth digit?
When would you have written six for […]
Think of a whole number. Square it. Subtract the number you first thought of. Is the answer odd or even?
Try this with other numbers. What do you notice? Can you explain why? Can you find different ways to explain (and prove) the result that you noticed. You might use what you […]
My car has number plate – S208VBJ.
Using my special code S208VBJ adds to 65.
Using the code every character, a digit or a letter, is separate.
Numbers are simply added together so that, in the first number plate 208 is 2 + 0 + 8 = 10.
Letters are translated into […]
If you change the order of these digits you can get 24 different numbers, for example 2547, 2574, 2745, … Can you find all 24 different numbers made by using each of the digits 2, 4, 5, 7 just once?
How many of these numbers have 2 in the thousands place? How many have 2 […]
Here you see the front and back views of a dodecahedron which is a solid with pentagonal faces.
Using twenty of the numbers from 1 to 25, each vertex can be numbered so that the numbers around each pentagonal face add up to 65.
The number F is the number of faces […]
This shape, which is constructed using four semi-circles, is called a Salinon.
If the radius of the larger blue semicircle is a and the radius of the smaller blue semicircle is b, what are the radii of the smallest semicircles?
What is the relationship between the area of the shaded region and the area […]
Investigate different triangles PQR where the angle QPR is 40 degrees. Choose your own angles at Q and R, for example someone might choose 90 degrees and 50 degrees and someone else 62 degrees and 78 degrees.
Accurately draw the internal bisectors of the angles at Q and R to meet […]
Look at the route the arrows follow in this diagram. Look away from the screen and try to describe their path.
Will the route pass through the point (18,17)?
If so, which point will be visited next? Explain how you found out.
How many points does the route pass through […]
A photographer is taking photographs.
She has to arrange the people in two rows one behind the other in order of height.
Each person at the back must be taller than the person directly in front of them.
Along the rows the heights must increase from left to right.
How many different arrangements […]
What is the sum of all the digits in all the integers from one to one million?
Don’t do a lot of tedious adding up – think mathematically!
Note: the digits in the integers from one to ten add up to 46
(not 55 because 10 contributes only 1 to this sum.)
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