Can You Help My Grandfather ? - Part 2

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Welcome back guys and sorry, my grandfather no longer needs help. In fact, thanks to some really smart guys my grandfather (virtual) has gotten the help he needed - or maybe the problem was too easy.

You may be wondering what the problem was but no need to over think, you can find it in my previous post.
Before we proceed to announce the winners - those that helped my grandfather, let's first give the answer to the problem presented in the post. The problem is given below.

Early this morning, my grandfather and I were having a conversation about great men of science, particularly in the 17th century. He seemed to be talking about one that was very amusing to him, this historical figure was amongst the leading experts in horology as at the time. According to my grandfather, when he was younger he so loved reading about certain great men of science that he also kept records of their date of birth and death in his head. But due certain circumstances such as old age, he seemed to have forgotten the year this particular historical figure died and he needs your help remembering this year. Can you help my grandfather figure out this forgotten year. The clues below may be of assistance.

The first three digits of this forgotten year is a number whose square root gives the first two odd numbers.

To get the last digit of this forgotten year, we need to find the last digit of the mathematical operation given below

5^140 (which reads 5 raised to the power of 140)

The first clue isn't that hard, all we need do is identify what the first two odd numbers are and they are 1 and 3. Since the square root of the number we are looking for is also a number, we should expect 1 and 3 to form that number. However, for the overthinkers it could be 31 or 13. Now, since the square root of what we are looking for gives either 31 or 13, we should expect a reverse operation to get this unknown number. As an illustration,
√a = 13 or √a = 31
a = 13² or a = 31²
a = 169 or a = 961

We however need a single number, that is, between 169 and 196. To help get the actual answer, we need to go back to the conversation between me and my grandfather, there's a part that talks about the 17th century. So therefore, it's likely the dude died in the 17th century. The first two digits of the forgotten year can be gotten from the 17 (in the 17th century) which is then 16 (17 - 1). We can compare this 16 with the first two digits of 169 and 961. The answer for the first clue is obviously 169.

For the second clue, finding the last digit of

5^140

We don't need to think too far or even use a calculator, as the calculator may be misleading. The reason being that your common calculator cannot give all digits of the above operation, this is probably due to it's memory. However, someone very observant would notice that even for lesser powers (natural numbers) of 5, the last digit of the corresponding operation always gives 5. Therefore we can assume and conclude that for all powers (natural numbers) of 5 the last digit of the resulting operation gives 5. However, for mathematical proof (for those mathematically inclined) you can use "mathematical induction" - see @mathowl's comment in the previous post.

Back to our riddle, the forgotten year is actually "1695" and the famous horologist who died in 1695 is none other than Christiaan Huygens.

In the same previous post it was stated that the image there (a grandfather clock) can be used. That particular image was placed there because the grandfather clock is also a pendulum clock which was invented by Huygens. With the Help the internet you could just search for the famous contributors to development of the pendulum clock and also search for the year they died, particularly in the 17th century.

Below are the winners

Till I come your way again next time, we thus conclude this episode of our game. My virtual grandfather also sends his regards, especially to the winners.

Thank you all once again for stopping by to read my jargons and also thank you @juecoree, @lemouth and the @Steemstem team for your valuable supports.

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