We spent our week trying to solve the Journeys in Numberland mathematical challenge. Here is our solution:
Whichever route or sequence you take, you will always get the same answer, as long as the grid is the same. This is because everytime there is a times and a divide or an add and a takeaway and everytime they cancel each other. For example if you go right for a x2 and left for a divide by 2, they cancel each other out.
For example:
3 x 2 = 6
but if you divide it back...
6 / 2 = 3 (which is just halving by the way! and x2 is doubling!) it just cancels out your calculation.
or
10 + 9 = 19
OPPOSITE
19 - 9 =10 tada!!! (It's like dividing and times, it's just undoing again, just like the undo button on your computer!)
Also, how they end up the same is because they're the same route but in a different way but they're just in a different order. But they still get into the same answer.