New Year Puzzle:In amagic square, the sum of numbers on each row, each column, and each diagonal is the same. Fill in the numbers in the following squares to make them become magic squares.

### Merry Christmas and Happy New Year

### Which is smaller? which is larger?

Today let us look at the following two tricky questions:

**Question 1:**Among these two numbers 4444 x 55555 and 5555 x 44444, which one is smaller? which one is larger?

**Question 2:**How about 5000 x 5000 and 4999 x 5001, which one is smaller? which one is larger?

### Vianney's awesome square!

- each entry is a square number: $$1=1^2, \quad25=5^2, \quad 49=7^2$$
- the sum of numbers on each row, each column, and each diagonal is the same.

### Pythagorean Identity

This year we will start a blog series about mathematical identities. Let us begin today with the Pythagorean Identity $$ a^2 + b^2 = c^2 $$

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