Numbering puzzle

3, 10, 24, 50, 120, 170, 288, ?

what comes at '?' ?

ANSWER :


2^2 - 1 = 3, 3^2 + 1 =10, 5^2 -1 = 24, 7^2 +1 =50, 11^2 -1 =120, 13^2 +1 =170, 17^2 - 1=288 and hence the next term is 19^2 + 1 = 362

Maths: Armstrong Numbers

Question: Divide the number 1301 into four three digit parts abc, def, ghi and jkl

so that

abc + def + ghi + jkl = 1301

and

abc = a^3 + b^3 + c^3
def = d^3 + e^3 + f^3
ghi = g^3 + h^3 + i^3
jkl = j^3 + k^3 + l^3




SOLUTION :

' This is related to “Armstrong Numbers”.

1301 = 153 + 370 + 371 + 407

These are the only 3 digit numbers that have this property.

The number 1729 (called Hardy Ramanujam number)

Why is the number 1729 famous ? Well, it all started from around a century back. There were these 2 famous mathematicians, G Hardy and Srinivasa Ramanujam (who was entirely untrained, but a remarkable mathematician) who were sitting in a hospital room (Hardy had come to visit Ramanujam).
Ramanujam asked Hardy about the taxi number that he came in, and Hardy mentioned 1729, calling it a boring number. Ramanujam disputed that,calling 1729 as a very interesting number, it is the smallest number expressible as the sum of two cubes in two different ways.
Which are the 2 ways?
10X10X10 + 9X9X9 = 1729
12X12X12 + 1X1X1 = 1729
There are no other numbers smaller than this which is the sum of 2 cubes.

The mysterious number 6174

I was roaming around the web, when I saw this particular web page, explaining the mystery of the number 6174. Read it to the end, and you will feel happy that you learnt something new.
So what's the mystery of the number 6174? Well, it's sort of like a mathematical puzzle. You need to do the following steps:
1. Take any 4 digit number where all 4 digits are not the same (so you can't select 9999), so for example, take 3456
2. Rearrange the digits to get the largest and smallest number: so you get 3456 and 6543
3. Subtract them, so you get 6543-3456 = 3087
4. Do this again with the resultant number, so you get 8730 - 378 = 8352
5. Again repeat 4, so you get 6174
6. Do it again, 7641-1467 = 6174
The number repeated itself, and will do so again and again, no matter which 4 digit number you take.
For 3 digits number, you get 495

Some maths calculations resulting in visual similarity

Sometimes maths can be real fun in terms of how some simple calculations can result in some visually interesting results. Take a look at some of the equations below, and you can't help but admire the way that these work out

Multiplication and addition with increasing numbers
0 x 9 + 0 = 0
1 x 9 + 1 = 10
12 x 9 + 2 = 110
123 x 9 + 3 = 1110
1234 x 9 + 4 = 11110
12345 x 9 + 5 = 111110
123456 x 9 + 6 = 1111110
1234567 x 9 + 7 = 11111110
12345678 x 9 + 8 = 111111110
123456789 x 9 + 9 = 1111111110


Multiplications with similar increasing numbers
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321


Another Magic of Math

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

Then... Check this out ...

1 x 18 + 1 = 19
12 x 18 + 2 = 218
123 x 18 + 3 = 2217
1234 x 18 + 4 = 22216
12345 x 18 + 5 = 222215
123456 x 18 + 6 = 2222214
1234567 x 18 + 7 = 22222213
12345678 x 18 + 8 = 222222212
123456789 x 18 + 9 = 2222222211

Generating chapter numbering in word

Q. I am writing a book using Microsoft Word and would like to skip numbering on chapter-division pages but resume numbering on the following page. How do I do this?

A. In current versions of Microsoft Word, one way to adjust page numbers within a long document is to make each chapter a separate section. You can then manually adjust the page numbers within that section.

To divide the document into separate sections, click your cursor at the point where you want to create a new section, say, at the end of each chapter, and then select the Break option from the Insert menu. In the Break box, you can specify where you want the new section to begin, say, "t" to follow continuously on the same page or "n" to start on the next page.

The dialogue box for adding page numbers is found under Word's Insert menu with the Page Numbers option. This box lets you choose where you want the numbers to appear on the page and how they should look. Click into each section to adjust the page numbers for that chapter.

Uncheck the box next to "Show number on first page" in the Page Numbers box. This will remove the page number from the first page of your new chapter, which should be the chapter division page.

Next, click the Format button in the Page Numbers box. Click the "Start at" button and type in the page number you want for the start of the new chapter. Even though it won't display the number on the page, Word will count the chapter division page and display the next number on the following page. If you don't want the chapter-division pages numbered or counted, start the page sequence one number earlier in the "Start at" box.

For example, your first chapter ends on Page 25 and you want to skip the number on the chapter division page and have the first real page of the second chapter be Page 26. In the Page Numbers box for the second chapter-section, click Format and then "Start at" Page 25. Word will count the unnumbered chapter division page as Page 25 and visibly number the first page of the second chapter as Page 26.

Fun number puzzle with birthday

Using a calculator with this puzzle might help

Take the number of the month you were born,
multiply by 4,
add 13,
multiply by 25, subtract 200,
add the day of the month on which you were born,
multiply by 2, subtract 40, multiply by 50, add the last two digits of the year in which you were born,
subtract 10,500.

Notice anything funny about your answer?

Did your math teacher teach you this?