I'm looking for a really hard math trivia question. Do anyone have a really good one(please include solution)?

Answer 1

How do you multiply two numbers together without using multiplication tables? You may only double or take half of the numbers.

Ancient Egyptian Method of Multiplication

The ancient Egyptians were not aware of the concept of multiplication tables as we are. The following method of multiplying numbers was developed by them to serve their needs.

For example, we will multiply 12 times 8. We all know the answer to this or --do we?

The ancient Egyptians used the following method. Start two columns; one begins with 12, the second begins with 8. The first column will be divided by 2; ignore the remainder; the number in the second column will double with each iteration.

Every place we have an even number in the first column we cross through the numbers in the first and second columns. Then, add the remaining numbers in the second column. This iterative process will work for any pair of positive integers.

½........X2
12.......8
6 ......16
3.......32
1.......64
total..96


A byproduct of the process is that the number in the first column, in this case 12, is converted to a binary number (base 2) in the following way:
In the first column every place there is an odd number developed in the halving process, replace with 1; for even numbers, replace with 0. Reading from bottom to top we have 1100 which is the binary equivalent of 12.


A byproduct of the process is that the number in the first column, in this case 12, is converted to a binary number (base 2) in the following way:
In the first column every place there is an odd number developed in the halving process, replace with 1; for even numbers, replace with 0. Reading from bottom to top we have 1100 which is the binary equivalent of 12.