Place The Numbers 5, 4: Fill & Download for Free

Step I: [Take only first 5 digits] A five digit number divisible by 5 can only end with '5'(0 is not allowed)=> Middle digit is 5. Number is _ _ _ _ 5 _ _ _ _Step II: All even digits should be even. because they'll be divided by an even number.Step III: [Take only first 8 digits]An eight digit number with 6th digit as even number, last 2 digit can have only 4 combinations, . These are 96, 16, 72, 32. Number will be as follows:(EDIT: Considering that it is divisible by 8 and 7th digit is odd)_ _ _ _ 5 _ 1 6 __ _ _ _ 5 _ 9 6 __ _ _ _ 5 _ 7 2 __ _ _ _ 5 _ 3 2 _Step IV: [Take only first 4 digits]A four digit number divisible by four ends only with 2 or 6. Keeping in mind that these number don't repeat only 4 Combinations are possible:(EDIT: Using the fact that 3rd digit is odd and is divisible by 4)_ _ _ 2 5 _ 1 6 __ _ _ 2 5 _ 9 6 __ _ _ 6 5 _ 7 2 __ _ _ 6 5 _ 3 2 _Step V: [Take only first 6 digits]For a number to be divisible by 6; 6th number should be even and last three digit should add up to make a multiple of 3. Only 4 Combinations possible_ _ _ 2 5 8 1 6 __ _ _ 2 5 8 9 6 __ _ _ 6 5 4 7 2 __ _ _ 6 5 4 3 2 _Step VI: Now only one even number is remaining for occupying 2nd place in each of the above combination. For example in Ist case: 4 is the only remaining even number to be consumed. The combination will go as follows:_ 4 _ 2 5 8 1 6 __ 4 _ 2 5 8 9 6 __ 8 _ 6 5 4 7 2 __ 8 _ 6 5 4 3 2 _Step VII: Total 10 combinations remain:1 4 9 2 5 8 1 6 _9 4 1 2 5 8 9 6 _3 8 1 6 5 4 7 2 _1 8 3 6 5 4 3 2 _3 8 1 6 5 4 7 2 _1 8 3 6 5 4 3 6 _1 8 9 6 5 4 7 2 _9 8 1 6 5 4 3 2 _1 8 9 6 5 4 7 2 _9 8 1 6 5 4 3 2 _Step VIII: Taking only first 7 digits of all of the above numbers. Only 3816547 is divisible by SevenComplete number 381654729 is divisible by 9.I am sure only 381654729 thus satisfies the answer.Feel free to comment.Edit: I didn't use computer to reach this result.

I want to ask a counter-question: in what sense are abstract objects not real?An abstract object, like the number 5, has no mass or location, no size or color or texture. And this, I conjecture, is the real reason so many people have trouble with the idea of abstracta being real, or in some way independent of us. The temptation to say that an abstraction, like the number 5, exists only in your mind, or in your brain if you want to be (pseudo)scientific about it, arises because it seems so strange for something to exist all by itself without being a concrete object that you can pick up with your hands, or maybe examine with some scientific apparatus.When I say that abstracta are real, I mean that they are mind-independent, which is to say that the number 4 would exist even if no humans had ever existed. Triceratops had 4 legs before we counted them. Our solar system had 1 star before we counted it. And so on. The mathematics of things, whatever they are, are not dependent on the human mind. Moreover, there is no “your” number 4 and “my” number 4, no “your” Pythagorean theorem and “my” Pythagorean theorem. There is only the Pythagorean theorem, and the square of two legs of a right triangle in a Euclidean plane equal the square of the hypoteneuse regardless of what we agree on. We can change the axioms we’re working with, or agree to define “triangle” differently, but none of this will change how right triangles work.Perhaps it would help to think of real abstracta like this: something is real if exists concretely, but something can also be real by being always true. It’s a fact that the set of integers does not contain a highest prime, and it seems to be beyond our power to change this. I suppose you could investigate some other branch of math where this isn’t true, but changing the subject doesn’t really help here.One last bit: the whole “numbers exist only in the mind” thing runs into some serious trouble when you consider it closely. The number 5 is a pattern of neural activation in my brain, sure. So do you have the same number 5 in your brain, an analogous pattern of neural activations? Yes? Okay, so an analogous pattern can be in two places at once. The “pattern” is now an abstraction, because it’s not a single concrete object somewhere, and you just pushed the problem back.

This question raises a bit of a philosophical question, that primary school doesn’t typically ask you to think about.Is the symbol the number?Think of the number 1.How many ways can you express it without using the lone symbol '1′?[math]3–2[/math][math]4–3[/math][math]5–4[/math][math](3–2) - (4–3) + (5–4)[/math][math](3–2) + (4–3) - (5–4)[/math][math](3–2)(4–3)(5–4)[/math]Just from this, you might even think I can just keep combining other symbols in an infinite number of expressions… all which represent the very same number.‘1’ is just a symbol that represents a number. But there are an endless number of ways to represent the number itself.To recap: the symbol, 1, is not the value that the symbol represents. There are many different ways to represent that symbol.Pi is also just a number. It is approximately equal to 3.14159… but the exact value cannot be written down as a finite decimal.This does not mean that pi is any less of a number. We just don’t have enough paper to write every digit of its decimal representation. And since 3.14159… ends up being such a useful number (it just starts poppling up all over the place), we have given it a specific name: pi. So that it has a very simple name.But still, pi is just the name we have given to a certain number. So, just like 1, there are endless ways to express the value of pi.My favorite is probably:[math]\sqrt{ \frac{6}{1^2} + \frac{6}{2^2} + \frac{6}{3^2} + \frac{6}{4^2} + … }[/math]Not so much because it’s especially simple, but because of the history behind this particular expression. Basel problem - WikipediaNow, you may think something like:Well, we can’t write pi down because it goes on forever. So I wanted an equation. But your expression above… how do I find the square root of an infinite number of fractions?Great question! Which I’m not going to answer, because the answer just won’t feel satisfying.But if you’re asking the question, you have a very good open question in your mind. You’re honing in on something that’s VERY peculiar about the real numbers that violates our common, day-to-day understanding about what kinds of numbers live between the integers… and how the hell do you “do” things infinitely. Very good questions, indeed…