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Mathematics can be quite interesting.

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It thrills to see the perseverance of both Shri sravna and Smt. VR. Very good analysis!

However, the special property of 2519 which I have in mind is illustrated below:

2519 divided by 2 leaves a reminder 1
2519 divided by 3 leaves a reminder 2;
2519 divided by 4 leaves a reminder 3;
2519 divided by 5 leaves a reminder 4;
2519 divided by 6 leaves a reminder 5;
2519 divided by 7 leaves a reminder 6;
2519 divided by 8 leaves a reminder 7;
2519 divided by 9 leaves a reminder 8;
2519 divided by 10 leaves a reminder 9.

That's it!


 
Yes Mr. C.L.N.

The 2519 can not be unique the way it was figured out to be.

The magic discovered by Mr. Sravna works for all numbers ending in 59

inducing the number 59!

5x9=45
5+9=14
54 + 14= 59

So 59 is the unique number making all the other numbers magical!

I thank all of you for this opportunity is have some harmless fun! :)
 
VR: It WORKS for the number 3459 but not for 2719!
Click to expand...

Of course it will work with any number ending in 9, madam. You must have made some simple mistake in verifying it for 2719.

Generally, any number with 9 in its unit's place can be taken to be N x 10 + 9, where N is a natural number.

Then, it can be also written as N X (9 +1) + 9, which is the same as (N X 9) + (N +9).

This is the solution Shri sravna has given and so can apply to any number ending in 9 (i.e., 9 at its unit's place).
 
I think we can write a general formula for number ending in any digit

For numbers ending in 9, we have (N x 9) + (1 x N ) +9
For numbers ending in 8 we have (N x 8) +( 2 x N) + 8

and so on,

The general formula being (N x M) + (( 10- M ) X N ) + M
where M is the ending digit.

Try for 6 ending say the number 1286
Here N= 128, M=6.
Thus, (128 x 6) + (4 x 128) + 6= 1286
 
A slight variant of my puzzle can be:

What is the smallest number which can be exactly divided by 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10?

(The answer is NOT 2519!)
 
H.Krishnamurthy said:
Mr. Sravana,
You can post the solution sir.
Sorry for not mentioning in my earlier post.
H.Krishnamurthy.
Click to expand...

OK, here's the solution

9-15 = 4-10 .

9-15 +25/4 = 4-10+25/4 .
This is ok . You are adding the same number to both the sides.

(3 - 5/2) aquare = (2-5/2) sqaure
This is ok too. You are just applying the formula, (a-b) aquare, to both the sides

Now you are taking the square root.

This is the problem

The RHS is (3- 5/2) square =0.5 square
and the LHS is (2-5/2) square = -0.5 square

Thus the squares are equal but not their square roots. So the dsicrepancy
 
Regarding 2519, it also seems to be the only four digit number such that

25 x 19 + 25 +19 =519

or (first two digits x last two digits) + (first two + last two) = last three digits
 
I Salute you all my friends for your Mathematics Knowledge.
I feel am a Kid in front of you all as far as the subject Mathematics is concerned.
Once again please accept my Salute ( or is it Namaskarams ).
H.Krishnamurthy..
 
Dear Mr. H.K.M!

When it comes to mathematics or sciences, we are all kids of different

ages climbing different rungs of the same ladder!

Nice of you to have brought in some harmless fun by activating our gray cells

where mud flinging and terrible temper tantrum (T3) have become the major

business of the day!

with best wishes,
V.R.
 
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I second Sri H.Krishnamurthy's statements...

Indeed a very interesting/informative thread and for me its bit confusing too, as my knowledge in mathematics got diminished after +2.

Just want to share a email that I received, to share with you all here, just for fun.

"THAT'S ENGINEERING"

The question was:

Prove that (2/10) = 2

1. The Science student said:
"This is Impossible"

2. The Commerce student:
"This is Wrong"

3. The Medical student:
"It's Strange!!, How it is Possible?"

4. The Engineering student: "It's so Easy!"

(2/10)

= Two/Ten

“T” is common, Hence = wo/en

Now,

‘W’ is the 23[SUP]rd[/SUP] Letter in English and ‘O’ is 15[SUP]th[/SUP];
Similarly,
‘E’ is 5[SUP]th[/SUP] and ‘N’ is 14[SUP]th[/SUP]

Hence, (wo/en) = (23+15)/(5+14)
= (38/19)
= 2

Engineers are never worried for:
What is the answer

 They will only ask:
Which answer do you want?

“That is an ENGINEER!!”





 
sravna said:
Regarding 2519, it also seems to be the only four digit number such that

25 x 19 + 25 +19 =519

or (first two digits x last two digits) + (first two + last two) = last three digits
Click to expand...

Refer above.

It also seems to me that there is one more four digit number which conforms to the rule

first two x last two + first two + last two. Tka e the last three digits. It conforms to the last three digits of the number. That other number is 5039. Applying the rule, 50 x 39 + 50 + 39= 2039

Interestingly the number 5040 is divisible by all single digit numbers.
 
Visalakshi Ramani said:
If 2520 is divisible by all integers from 1 to 10

then 5040 which is a multiple of 2520

will definitely be divisible by all the integers.
Click to expand...

Yes, but what I am saying is it conforms to the rule

(first two X last two).... which I have mentioned in the previous post. I am pointing to a coincidence.
 
sravna:Interestingly the number 5040 is divisible by all single digit numbers.
Click to expand...

Not only 5040, any multiple of 2520 wil have this characteristic! Therefore, the uniqueness of 2520 lies in it being the smallest number divisible by all single digit natural numbers!

Ok. Here is another famous addition puzzle:

S E N D + M O R E = M O N E Y

'SEND' and 'MORE" are two 4-digit numbers, which when added give 'MONEY', which is 5-digit number! Here, each alphabet stands for a digit. Same alphabet means same digit. There is only one solution and it can be worked out by pure logical reasoning!
 
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CLN said:
Not only 5040, any multiple of 2520 wil have this characteristic! Therefore, the uniqueness of 2520 lies in it being the smallest number divisible by all single digit natural numbers!

Ok. Here is another famous addition puzzle:

S E N D + M O R E = M O N E Y

'SEND' and 'MORE" are two 4-digit numbers, which when added give 'MONEY', which is 5-digit number! Here, each alphabet stands for a digit. Same alphabet means same digit. There is only one solution and it can be worked out by pure logical reasoning!
Click to expand...

9567 + 1085 = 10652

Regards,

narayan
 
There is an interesting tidbit about this "SEND + MORE = MONEY" puzzle. When I said SEND and MORE are 4-digit numbers and MONEY is a 5-digit number, it is automatically (and rightly too!) taken by any one that the left-most digits in these three numbers cannot be zero. But if this vital condition is not applied, the uniqueness of the solution is lost and there are several solutions to the puzzle! Any takers?
 
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