#1 To find the longest side of a right-angled triangle (the hypotenuse), you square the other two sides, add them up and find their square root.
#2 To make a numerical palindrome (a number that, when written backwards, reads the same number, or a mirror number), take a number, write it backwards, and add them up. Do this as many times as you need and you shall get a mirror number!
12 + 21 = 33 ( mirror number )
154 + 451 = 605 + 506 = 1111 ( mirror number )
239 + 932 = 1171 + 1711 = 2882 ( mirror number )
#3 (6 × 9) + (6 + 9) = 69. Simple but effective
#3 If you shuffle a pack of cards well, chances are that combination of cards has never been shuffled before. This is because since there are 62 cards in a deck, there are 64! ways combinations they can be put in. Now,! means factorial (or in nerdy language n(n-1)!), which can be used to determine how many ways you can arrange something. In short terms, the factorial of a number is a number times by itself, but every time you times it, 1 is deducted from it, until the number goes down to one. This means 4! would be 4 factorial which is 4 x 3 x 2 x 1 which is 24. This means there are 24 ways to arrange 4 objects. The simplest explanation of how this works is to imagine 4 carrots (labelled C! to C4) and a hungry rabbit. How many possibilities are there that the rabbit will eat the carrots?
Let’s say the rabbit first eats C3( it can be any but we will use C3 as an example. Now there are 3 carrots left. Now, let’s say the rabbit eats C2. Now there are 2 carrots. You can see where this is going and is actually quite simple to grasp, as there are 4 different carrots the rabbit can eat at first( let’s call this 4), then once he eats it there are 3, then when he eats that, there are 2, then that 1. The number of combinations is 4x3x2x1
You can apply this to any number and any object.
Now – back to our question.
If there are 64 cards and we want to find the number of combinations that you can arrange the cards, you work out 64! which is 64x63x62x61 and so on until 1. The answer is that you have 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000 ways to arrange the cards!