Solve the Arithmetical Teaser: 100-999 Integer

  • Thread starter Galileo
  • Start date
In summary, man 1 gives man 2 an integer from 100 to 999 and tells man 2 to think of the number and to repeat it in his head. man 2 gets 501 and man 1 tells man 2 to divide 501 by 13. man 2 divides 501 by 7 and gets 5511. man 1 tells man 2 to divide 5511 by 11 and gets 50111. man 1 tells man 2 to multiply 50111 by 1000 and get the result of 1001. 1001X = 1000000. So, every integer from 100 to 999 has this property.
  • #1
Galileo
Science Advisor
Homework Helper
1,995
7
This one is actually quite simple once you see it.

Consider the following converation between man 1 and man 2:

Man 1: 'I have a puzzle for you. First, pick an integer from 100 to 999 in your head.'
Man 2: 'Uuhhm. Well.. okay. (thinks: I`ll take 501, 'cuz that me lucky number.')
Man 1: 'Okay, consider the number that you get by repeating the number in your head once. So if you had 123, you should have 123123.'
Man 2: 'Okay. (That'll be 501501)'
Man 1: 'Now divide that number by 13.'
Man 2: '..wait a sec... okay. Fortunately it's an integer. (that's 38577)'
Man 1: 'Divide that number you got by 7'
Man 2: '..(that'll be 5511).. okay. Luckily another integer!'
Man 1: 'Now divide it by 11.'
Man 2: '(5511/11 is..eh 501). Hey, I get the number with which I started.'
Man 1: 'Really? I suppose you made a good choice at the start. My question is: How many integers from 100 to 999 have this property?'

So, how many integers are there from 100 to 999 which have this property?
 
Physics news on Phys.org
  • #2
Surely I'm screwing up somewhere, but 1001 = 13*11*7, so they all do .
 
  • #3
Hmmm,
[tex]\frac{1001}{7*11*13}=1[/tex]
no idea at all. Guess, I'll just have to try them one by one.
 
  • #4
Galileo said:
So, how many integers are there from 100 to 999 which have this property?

The answer is all of them (900). This works because taking any number like 501 and making it 501501 is the same thing as this:

Assume the number you chose is "X". So X = 501

(X*1000)+X is the formula that gives you 501501.

1000X +X = 1001X

1001X/1001 = X

Works everytime regardless of X up to 999.
 
  • #5
Mwa. I knew it was too easy. Oh well...
 
  • #6
well, yes it is quite easy, in fact i had read this in a book quite a few years back.


i think i should look for that book, maybe i can post some good questions from that book too.
 

1. How do I solve the arithmetical teaser: 100-999 Integer?

To solve this teaser, you will need to follow the basic principles of arithmetic. Start by subtracting the smallest number from the largest number, which in this case is 100 from 999. This will give you 899. Then, divide this number by the difference between the first and last digits of the original numbers, which is 9. Finally, add this quotient to the original numbers, 100 and 999, to get your final answer of 1099.

2. Can the arithmetical teaser: 100-999 Integer be solved using a different method?

Yes, there are multiple methods to solve this teaser. For example, you can start by adding the last digits of the original numbers, which is 0 and 9, to get 9. Then, add this number to the first digits of the original numbers, which is 1 and 9, to get 109. Finally, add the middle digit of the original numbers, which is 0, to get your final answer of 1099.

3. Is there a specific order in which the numbers should be subtracted in the arithmetical teaser: 100-999 Integer?

No, you can subtract the numbers in any order. The result will be the same regardless of the order in which you subtract them. However, it is recommended to subtract the smaller number from the larger number to avoid getting a negative answer.

4. Can the arithmetical teaser: 100-999 Integer be solved using a calculator?

Yes, you can use a calculator to solve this teaser. Simply enter the equation as stated, 999-100, and then divide the result by 9. The calculator will give you the final answer of 1099.

5. Are there any tips or tricks for quickly solving the arithmetical teaser: 100-999 Integer?

One tip is to look for patterns in the numbers. In this teaser, you can see that the difference between the first and last digits of the original numbers is always 9, and the middle digit is always 0. This can help you quickly determine the final answer without having to go through the entire mathematical process.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
19
Views
1K
  • Programming and Computer Science
Replies
17
Views
976
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Replies
3
Views
13K
Replies
9
Views
2K
  • Math Proof Training and Practice
2
Replies
60
Views
8K
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
10K
Replies
10
Views
33K
Back
Top