The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
There were a number of good solutions to this
problem and I have picked several to illustrate the different
First Fred and Matt from Albion Heights sent
in a solution, which I rather liked. They have not explained why
they did not try 1/3 as the first fraction or give full reasoning
for why they knew they had a largest value, but the argument as far
as it goes is a good one. I have added some examples below to
illustrate what they said in a little more detail. I have included
a solution based on the one from Tom or STRS, which was similar to
that of Curt from Reigate School . Andrei, of Tudor Vianu College,
also looked for solutions using a spreadsheet and sent in a program
in C++ to search for soultions. I have included this below.
Well done to all of you.
First Fred and Matt's approach to get us
Andrei's program (I haven't tested