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A flipping fortune

Posted by Chris under MathsChallenge (32 Responds)

Starting with $1, you begin flipping a coin. Each time it comes up heads you double your money.  You stop when the coin lands tails up, but you keep all the money.  On average, how much money do you expect to have after one game.  I’ve no idea where the money is coming from.

Example.  You flip HHT, you end up with $4 (including the initial $1).

Seating arrangements

Posted by Chris under MathsChallenge, Tom (24 Responds)

Thirteen friends decide to go to the movies.  In the theater there are rows of 13 seats.  For some stupid reason they decide that the first person to enter the row may sit wherever he chooses.  The second person must sit on either side of him with no empty seat between.  The third person may sit on either side of the first two as long as no empty seat is between them.  This procedure continues until all are seated.

How many different seating arrangements are possible?

Speed of Light in Holy Quran

Posted by TheWyvern under Tom (4 Responds)

This is the answer to my post “The Speed Of  Light.. Read Carefully ..

Behind a great verse, there is a hidden signal to the speed of light. Recently that signal was discovered by scientists, God says :( And verily, a day with your Lord is as a thousand years of what you reckon.)(Sûrat Al-Hajj- verse 47)

In 1969, and during their trip to the moon the astronauts put a glass mirrors on the surface of the moon and scientists on earth sent a Laser beam to be reflected on these mirrors to back again to the earth . By that they calculated the precise distance between earth and moon.
If we observe the moon from outside the solar system , we can see that moon is revolving a complete round around earth every 27.3 day , but because earth revolves around itself so we see the moon is completing the round every 29.5 day

The moon revolves around earth a complete round every month, but because earth is also revolving around itself and in the same direction so that we see the month is 29.5 day but in fact it only takes 27.3days for the moon to complete the round. The question is what is the traveled distance by the moon around earth in 1000 year?

A Muslim scientist put forward an idea which is: the holy verse refers to two equal times and that is some kind of the relatively. God be He blessed says: (And verily, a day with your Lord is as a thousand years of what you reckon) (Sûrat Al-Hajj- verse 47), so we have a day and a one thousand year, how can we make them equal? And what is the common factor?

Scientists consider the speed of light is a distinguished speed and there is no object can be able to reach that speed. So whenever the speed of an object increases therefore the time for that object will slow down. Therefore if any object reached the speed of light, the time will stop for that object. that is the summary of Theory of relativity.

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A photo for the real distance between moon and earth .The moon revolves around earth in a non- circular (Oblate) orbit .Distance between both of them is about 384 thousand km. Moon revolves around earth in a speed of 1 km / second. According to the International standards, speed of the light in the empty space is 299792 km/second.

If we called the mentioned day in the verse with “the cosmic day” to distinguish it from our ordinary day so according to the holy verse (And verily, a day with your Lord is as a thousand years of what you reckon) we can write the equation as the following:

“One cosmic day” = “one thousand year (according to our calculations)”

So, there is a hidden relationship between length of the day and length of the one thousand year. What is the relation?

1. Calculation of the length of the one thousand year

The determination of months and years is based on the movement of the moon. so the month for us is a one complete round for the moon around the earth. We know that moon revolves one round every month around earth, so it will be 12 rounds in the year. God says :( Verily, the number of months with Allah is twelve months (in a year)) (Sûrat at-Taubah- verse 36)

In a simple calculation based on the real month, the moon travels 2152612.27 km around earth in compete round. This distance represents the length of the orbit that the moon takes while a complete round during one month.

So the distance per year is: 2152612.27 × 12 = 25831347 km

And in one thousand year is: 25831347 × 1000= 25831347000 km

2. Calculation of the length of the one day

The day is 24 hours and in seconds it is: 86164 seconds according to the International standards.

Right now, we have the value of one thousand year “25831347000km” which is the distance” and we have the length of the day “86164 second” which is “the time“.

Hence, to realize the hidden relation between distance and time we can use the known formula:

Speed = distance ÷ time

After applying these figures in the formula we can see the surprise which is:

The cosmic speed = 25831347000 ÷ 86164 = 299792 km\ second which is exactly the speed of the light.

Therefore we can realize that the signal in the holy verse is the speed of light by liking “the one day” and “the one thousand year”. this is a scientific precedence for the Qur’an and it wouldn’t be a coincidence.


Here are some questions that the reader of this article may face which can be summarized in the following:

1. Why we considered this verse as a signal for speed of light?

2. Why the Qur’an did not speak directly about the speed of light?

3. Does this research say that the divine order descends in the speed of light?

In fact the Qur’an contain many hidden signs which were Unintelligible in the previous years but at the suitable time it can be explained and became clear to understand the miracle and to be an evidence that message of Islam is sincere.

The holy verse linked between the day and the one thousand year and the relation is the value of the speed of light which is 299792, how can we explain the existence of that number in the Qur’an?

3 squares

Posted by Chris under MathsChallenge (8 Responds)

I’ve pinched this from the old ToM site.

There are three distinct integers which have the property that the sum of any two of them is a perfect square. What are they ?

There is more than one solution.

Flipping coins

Posted by Chris under MathsChallenge (36 Responds)

It’s ages since I’ve seen this one.

After flipping two coins, at least one of them shows heads. What is the probability that the other one also shows heads?

Average number

Posted by Chris under MathsChallenge (30 Responds)

If the probability of an event happening in one trial is p, the average number of trials needed to get the event is 1/p. Prove it.

Tall tail

Posted by Chris under Tom (8 Responds)

n people are standing in a queue. On average, how many of them can (truthfully) say that they are taller than everyone ahead of them?

NB The person at the front of the queue, can say that he is taller than everyone ahead of him.   Assume that they are able to accurately determine their heights.

Double trouble

Posted by Chris under MathsChallenge (18 Responds)

Five schoolchildren were weighed in pairs.  Their (combined) weights were:
129, 125, 124, 123, 122,121, 120, 118, 116 and 114 lbs.  What were their individual weights?

Complete the sequences

Posted by Karys under Tom (1 Respond)

I) 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, …
II) 1, 2, 4, 8, 16, 31, … (not 32)
III) 1, 25, 23, 13, 3, 14, 15, 16, 8, …

Even rows

Posted by Karys under Tom (5 Responds)

In a 6×6 grid of crosses :

x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x

1) Remove 6 xs, so that in each column and each row has an even number of xs. Try removing 8 xs instead of 6.

2) How many such possible combinations are there ?