Can you solve?
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The mathematical term “googol” was invented in 1920 by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. A googol is 10100, which means it is written as 1 followed by one hundred zeroes.
The fact that it can be written in such a compact form, 10100, is deceiving, because it represents a phenomenonally gigantic number of mind-blowing proportions. A googol is about one hundred billion billion times bigger than the number of particles in the visible universe (1080).
Although the company and search engine Google is spelt differently, it based its name on the huge number googol, because its ambition was to provide users with huge amounts of information.
What is googol squared?
What is √(googol)?
Each statement is either true or false. How many of the following statements are true?
1. The answers to statements 2 and 3 are different.
2. The answers to statements 3 and 4 are different.
3. The answers to statements 4 and 5 are different.
4. The answers to statements 5 and 6 are different.
5. The answers to statements 6 and 7 are different.
6. The answers to statements 7 and 8 are different.
7. The answers to statements 8 and 1 are the same.
8. The answers to statements 1 and 2 are the same.
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If the smallest equilateral triangle (light green) is 1, what other numbers can you see?
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Pick any 4 digit number (as long as the digits are not ALL the same).
Put the digits in ascending order and descending order to create two numbers.
Subtract the small number from the big number, to create a next stage number.
Then repeat the process with the new number
Eventually you end up with 6,174.
Alex has 25 discs that are black on one side and white on the other. He arranges them on a 5 x 5 grid so that all the white sides are showing.
A move consists of taking any three consecutive discs in a row or column and flipping them over. You want the discs to make the checkerboard coloring shown below.
From the initial all-white position, what is the smallest number of moves needed to get to the checkerboard position?
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So for a number to be happy, just take the digits, square each digit and add all the squares to create a new number. Then repeat the process with the new number, and continue until you end up with the number 1 or find the numbers stuck in a repeating loop that does not contain 1.
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UKMT volunteer Fraser Heywood kindly shared this video of his favourite mathematical puzzle with us. The Tower of Hanoi is a mathematical puzzle and a recursive algorithm, where the objective is to move an entire stack of disks from the source position to another position.
The three rules are:
- Only one disk can be moved at a time.
- A disk can only be moved if it is the uppermost disk on a stack.
- No larger disk may be placed on top of a smaller disk.
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A circle is inscribed in an equilateral triangle and an equilateral triangle is inscribed in that circle. What is the ratio of the areas of the two triangles?
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