What fractions can you find between the square roots of 65 and 67?
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
Part One : Pick two
numbers as multipliers (factors) to multiply together, say $37$ and
$51$. Choose some of the values from $1, 2, 4, 8, 16, 32, 64$ and
$128$ to make a sum equal to each of those numbers. For example $37
= 32 + 4 + 1$ and $51 = 32 + 16 + 2 + 1$
Incidentally, could $37$ or $51$ have been made in another way
Now select the side numbers needed to make the factors you've
chosen and press the "press when ready" button to begin.
Next click the counters in the grid one by one to see them move
towards the bottom line.
Finally click the counters remaining in the bottom line to
compile an answer (product) for your multiplication question.
" I found this technique fascinating.
Is there a way of inverting the process, i.e. Factorising. Starting
with particular circles on the bottom line, and finding some
process which could create the two factors you started with " ?