# Daily Quiz: Wednesday 28th July 2021 : The Fibonacci Sequence Quiz

### #1. Let's begin with a spot of math- it has been mathematically proven that the recurring decimal 0.999... (with an infinite number of 9s) is *exactly* equal to ___ .

Although it may seem counter-intuitive, it is indeed true that 0.999… represents *exactly* the same number that we generally represent by the familiar symbol “1”. For the mathematically inclined, here’s one of the many proofs of the same, simple but elegant (courtesy Wikipedia): Consider c = 0.999… Multiplying by 10, 10c = 9.999… Subtracting the two equalities, 10c – c = 9.999… – 0.999… i.e. 9c = 9 i.e. c = 1 (Q.E.D.).

### #2. Several religions, such as Judaism and Islam, are said to be 'monotheistic'. How many 'gods' does each of these believe in?

‘Monotheism’ indicates a single God. Belief in a more than one God is called ‘polytheism’. An example of a polytheistic religion is Hinduism, where the scriptures make references to 330 million (330,000,000) gods!

### #3. All natural numbers (1, 2, 3, 4, 5...) can be grouped as 'odd' and 'even'. 'Even numbers' are specifically those numbers which, when divided by ___, give a remainder of zero.

When even numbers are divided by 2, there is never a remainder, unlike odd numbers, which give a remainder of 1. Even numbers include the numbers [2, 4, 6, 8…], and odd numbers include [1, 3, 5, 7…]. In Chinese culture, two is said to be a ‘good’ number. There is a saying in Chinese: “good things come in pairs”.

### #4. A 'duo' is a group of *two* people or things. For example, Batman and Robin are sometimes called the 'Dynamic Duo'. But how many are there in a *trio*?

The term ‘trio’ is most common in music, to refer to a group of three musicians. The word ‘threesome’ is an alternative. It is also used for musical instruments; for example, the violin, viola and the cello form the ‘string trio’.

### #5. The UN Security Council has 15 members in all. Out of these, how many are *permanent* members, enjoying veto powers?

Out of the 15 members, 5, namely France, Russia, China, the US and the UK, are permanent members. The other 10 are elected from the General Assembly for a period of 2 years. The 5 permanent members enjoy ‘veto’ powers, which means that each one of their sanction is a must for the Security Council to make decisions on ‘substantial’ matters.
More can be found out here: http://www.un.org/Docs/sc/unsc_members.html

### #6. Complete the lyrics for the famous Christmas song, "The Twelve Days of Christmas": "___ maids a-milking..."

The last line of the song goes like this: “On the twelfth day of Christmas My true love gave to me Twelve drummers drumming, Eleven pipers piping, Ten lords-a-leaping, Nine ladies dancing, Eight maids a-milking, Seven swans-a-swimming, Six geese-a-laying, Five golden rings, Four calling birds, Three French hens, Two turtle doves, And a partridge in a pear tree.” Unfortunately, if in today’s world, our ‘true love’ gave us all of these, we’d be kicked out of our house by our landlord / neighbours / the police. “MAD” magazine once published a really funny feature that speculated the effects of being gifted such presents in the modern world.

### #7. This number is considered 'unlucky' by most cultures, but is 'lucky' for traditional Chinese people. At the Last Supper, this was the number of people (including Christ) who were present. A 'baker's dozen' has this number of loaves. Which number am I talking about?

‘Triskaidekaphobia’ is the unreasoned fear of the number thirteen. Because of this, some tall buildings call the 13th floor Floor 12a or something similar, and in many hotels, the 13th room is called Room 12a.

### #8. The popular card game 'Blackjack', known as 'Pontoon' in the UK, is also called ___.

In most parts of the United States, one must reach the age of 21 to gain the right to drink alcohol. 21 is also the number of dots on a standard cubical die (1 2 3 4 5 6). 21 is a “Harshad Number”, which means it is perfectly divisible by the sum of its digits (2 1).

### #9. The element Selenium (Se) has an electronic configuration of '2-8-18-6'. What is its atomic number?

From the electronic configuration (2-8-18-6), we can understand that there are 2 electrons in the first shell, 8 in the second, 18 in the third, and 6 in the fourth. Adding these together will give us the total number of electrons present in an atom of Se, which is the atomic number. 2 8 18 6 = 34. And so, the atomic number of Selenium is 34.

### #10. Now, if you've noticed the pattern which the answers in this quiz are forming, you should be able to get this one! What is the 7th root of 1522435234375?

Other accepted answers: fifty-five  fifty five

To get the answer, we first factorise 1522435234375:

1522435234375 = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 11 * 11 * 11 * 11 * 11 * 11 * 11

Taking the 7th root of both sides,

(1522435234375)^(1/7) = (5 * 5 * 5 * 5 * 5 * 5 * 5 * 11 * 11 * 11 * 11 * 11 * 11 * 11)^(1/7)
=&amp;gt; (1522435234375)^(1/7) = 5 * 11
=&amp;gt; (1522435234375)^(1/7) = 55

…which is the answer! But wait- what about the pattern formed by the answers? Which gives a simpler way of obtaining the answer…

===
Let’s take a look at the answers of questions 1 to 9:

Q1: 1
Q2: 1
Q3: 2
Q4: 3
Q5: 5
Q6: 8
Q7: 13
Q8: 21
Q9: 34

From these answers, you’ll notice that each answer (with the exceptions of the first and second ones) is the sum of the two answers that precede it. For example, ans3 (2) = ans1 (1) ans2 (1). Similarly, ans7 (13) = ans 5 (5) ans 6 (8).

In the same manner, answer 10 is the sum of answers 8 and 9: the sum of answer 8 and answer 9 = 21 34 = 55, which is the answer!

This special sequence of numbers is known as the *Fibonacci Sequence*. This sequence was first described by Leonardo of Pisa, a.k.a. Fibonacci, in 1200 A.D., to describe the growth of (an idealised) rabbit population!

## Results

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