Maths Puzzle

[Orior]

How come something can add up to two different values?

Take the sum below

      1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ...

By adding brackets it becomes

     (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + ...

which obviously equals zero.

But if i place the brackets slightly differently it becomes

     1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...

which obviously equals 1.


Stange eh? (Yes I am)

[Fear ón Srath Bán]

How come something can add up to two different values?

Take the sum below

      1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ...

By adding brackets it becomes

     (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + ...

which obviously equals zero.

But if i place the brackets slightly differently it becomes

     1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...

which obviously equals 1.


Stange eh? (Yes I am)

Should be:

1 + (-1 + 1) + (-1 + 1) + (-1 + 1)  - 1

= 0

It's the changing of the numbers that f*cked you up! 

[IolarCoisCuain]

Good counting a Srath Bhánaigh. There are four -1's in the first sequence, matching the four +1's, but only three in the second, bracketed, sentence, hence the disparity.

Must try harder Orior I'm afraid.

[under the bar]

Orior that's as bad as some Armagh people who think that 1 is equal to 3. 

[armaghniac]

1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ...

This might depend on whether infinity is an odd or even number!

Orior that's as bad as some Armagh people who think that 1 is equal to 3.

Many people do, we are all good Catholics.

[under the bar]

Orior that's as bad as some Armagh people who think that 1 is equal to 3. 

Many people do, we are all good Catholics.

[Orior]

Orior that's as bad as some Armagh people who think that 1 is equal to 3. 

It is, for large values of 1.

[Orior]

Okay, here's another (old famous one)

The Tortoise challenged Achilles to a race, claiming that he would win as long as Achilles gave him a small head start. Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow.

"How big a head start do you need?" he asked the Tortoise with a smile.

"Ten metres," the latter replied.

Achilles laughed louder than ever. "You will surely lose, my friend, in that case," he told the Tortoise, "but let us race, if you wish it."

"On the contrary," said the Tortoise, "I will win, and I can prove it to you by a simple argument."

"Go on then," Achilles replied, with less confidence than he felt before. He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.

"Suppose," began the Tortoise, "that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?"

"Very quickly," Achilles affirmed.

"And in that time, how far should I have gone, do you think?"

"Perhaps a meter – no more," said Achilles after a moment's thought.

"Very well," replied the Tortoise, "so now there is a meter between us. And you would catch up that distance very quickly?"

"Very quickly indeed!"

"And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?"

"Ye-es," said Achilles slowly.

"And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance," the Tortoise continued smoothly.

Achilles said nothing.

"And so you see, in each moment you must be catching up the distance between us, and yet I – at the same time – will be adding a new distance, however small, for you to catch up again."

"Indeed, it must be so," said Achilles wearily.

"And so you can never catch up," the Tortoise concluded sympathetically.

"You are right, as always," said Achilles sadly – and conceded the race

[Mario]

This is not a puzzle, 3 x 3 = 9 but 3 + 3 = 6, your just changing the symbols

[Orior]

This is not a puzzle, 3 x 3 = 9 but 3 + 3 = 6, your just changing the symbols

No i didnt.

Anyway, symbols cannot be changed under the Flags and Emblems Act.

[whiskeysteve]

Brad Pitt is thick

[Hound]

This is not a puzzle, 3 x 3 = 9 but 3 + 3 = 6, your just changing the symbols

No he didnt change any symbols, just left out a -1.
In the first there are 4 positives and 4 negatives, thus equals zero.
In the second there are 4 positives and 3 negatives, thus equals 1.

[Orior]

This is not a puzzle, 3 x 3 = 9 but 3 + 3 = 6, your just changing the symbols

No he didnt change any symbols, just left out a -1.
In the first there are 4 positives and 4 negatives, thus equals zero.
In the second there are 4 positives and 3 negatives, thus equals 1.

Yeah but, no but, yeah but, no but, yeah but, no but, yeah but, no but, yeah but, the point is that the series continues ad infinitum.

So it doest matter where I end the written sequence.

[Homer]

not a puzzle but...

10² + 11² + 12²  =  13² + 14²

[muppet]

Get a piece of paper.

Insert any mathematical function around the numbers 4 4 4 4 to complete the following and make the equations true:

4444 = 0
4444 = 1
4444 = 2
4444 = 3
etc.

You must complete them in sequence, no skipping a number.

You may not insert other numbers and must use four 4s in each line.

Remember if it is a mathematical function, you can use it.

Start your stopwatch and see how many you can do it 10 minutes.

Have fun.