But some random facts were easy to memorize, for example that the chessboard has 64 fields. I had problems with 6×9 and 7×8 though, always confused about which one was 54 and which one was 56.
Similarly 8x7 I can't tell you but 7x8=56 in my brain feels like a little "rhyme" I just need to repeat and I have the answer.
That's also how I remember (somewhat) arbitrary passwords. If it "flows" well almost like a rhyme and can be typed fluently I'll remember. Actual arbitrary ones don't work as well.
And then I just remembered that 7x8 is "that other difficult number", because by that time I already remembered that 54 and 56 are the two most difficult numbers in the multiplication table. :)
Btw, same here, 9x6 and 7x8 feels much more natural than the other way round.
- You want to compare two products: in this case 6x9 and 7x8.
- And in each product, if you add the two numbers together, you get the same result. In this case, 6+9 = 7+8.
Then the product will be larger for the pair of numbers that are closer together. So 7x8 > 6x9. That might help you remember which is 56 and which is 54.
You typically see this in a word problem where you are given a fixed amount of fence and you have to enclose the largest rectangular area. The answer is to use a square area (two sides being equal). If the problem has constraints that prevent the sides from being equal, then you pick the length and width to be as close to each other as possible.
In case you want to transfer the geometric intuition to an algebraic proof: If the sum of the two side lengths is 2m, then the two side lengths can be written as (m+n) and (m-n) for some positive n. If you multiply the two, you get (m+n)(m-n) = m²-n². To maximize the product, you need n to be as close to 0 as possible - i.e. for both sides to be as close to each other as possible.
And I don’t have a good memory either.