Degen's eight-square identity
Okay little one, today we're going to talk about something called "degen's eight-square identity." It's a pretty special math formula that is used to solve some tricky problems.
Imagine you have a square. A square is a shape that has four equal sides, like the kind you might see on a piece of paper. Now imagine you split that square into eight smaller squares, kind of like a tic-tac-toe board.
Degen's eight-square identity is a way of figuring out how to add up all the numbers in those eight squares. But instead of just adding them up one by one, we use a special formula to make it easier.
The formula goes like this: Take the number in the center square and multiply it by 4. Then add up the four numbers in the corners and multiply each one by 3. Finally, add up the four numbers in the middle of the sides and multiply each one by 2.
So let's say we have the numbers 1, 2, 3, 4, 5, 6, 7, and 8 in the eight squares. We can use degen's eight-square identity to add them up like this:
- Multiply the number in the center (5) by 4: 5 x 4 = 20
- Add up the four corner numbers, each multiplied by 3: 1x3 + 4x3 + 7x3 + 8x3 = 60
- Add up the four middle-side numbers, each multiplied by 2: 2x2 + 3x2 + 6x2 + 7x2 = 36
Now we just add up those three numbers: 20 + 60 + 36 = 116. So the total of all the numbers in the eight squares is 116.
See how easy that was? Degen's eight-square identity can help us quickly add up any group of eight numbers arranged in a square like this. Pretty cool, huh?
Imagine you have a square. A square is a shape that has four equal sides, like the kind you might see on a piece of paper. Now imagine you split that square into eight smaller squares, kind of like a tic-tac-toe board.
Degen's eight-square identity is a way of figuring out how to add up all the numbers in those eight squares. But instead of just adding them up one by one, we use a special formula to make it easier.
The formula goes like this: Take the number in the center square and multiply it by 4. Then add up the four numbers in the corners and multiply each one by 3. Finally, add up the four numbers in the middle of the sides and multiply each one by 2.
So let's say we have the numbers 1, 2, 3, 4, 5, 6, 7, and 8 in the eight squares. We can use degen's eight-square identity to add them up like this:
- Multiply the number in the center (5) by 4: 5 x 4 = 20
- Add up the four corner numbers, each multiplied by 3: 1x3 + 4x3 + 7x3 + 8x3 = 60
- Add up the four middle-side numbers, each multiplied by 2: 2x2 + 3x2 + 6x2 + 7x2 = 36
Now we just add up those three numbers: 20 + 60 + 36 = 116. So the total of all the numbers in the eight squares is 116.
See how easy that was? Degen's eight-square identity can help us quickly add up any group of eight numbers arranged in a square like this. Pretty cool, huh?
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