These are two questions from Math for Elementary Teachers and they have me stumped.

You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins?

The product of the diagonals of any 2x2 matrix in the base 10 multiplication table are equal. Why?

Hi,

The first question is not mathematics, it is a misleading English sentence. If "one of the coins is not a nickle", the other one might be a nickle.

Each entry in the multiplication table is the product of two numbers, the row number and the column number. For example in the piece of the table below I have rows 12 and 13 and columns 15 and 16.

 15 16 12 13 ... ... ... ... ... ... ... ... 12x15 12x16 ... ... 13x15 13x16 ... ... ... ... ... ...

Thus the product of the entries in either diagonal is the product of four numbers. Consider any 2x2 matrix where the rows and columns are adjacent and focus on the upper left corner of the matrix. Call its row number row number and its column number column number. Then the product along the main diagonal (upper left to lower right) is

(row number) x (column number) x (row number + 1) x (column number + 1) Using the same names what is the product along the other diaginal?

What changes if the rows are not adjacent? If the columns are not adjacent? If neither are adjacent?

Penny

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