find numbers whose product of digits is 6 times the sum of the digits

find numbers between 100-999, whose product of digits is 6 times the sum of the digits example 347 would be a number return because 3x4x7=6(3+4+7). I need to use a for-end loop to accomplish this. How can I do this?

[Walter Roberson]

Hint:

If you have arrays A, B, C, then

mask = A.*B.*C == 6.*(A+B+C);

[John D'Errico]

It looks like there are two basic sets of digits in that range of numbers that solve the problem. That is, any combination of the digits {3,4,7} works, as well as any combination of the digits { , , }. No, I'm not going to tell you the other set. There will be 12 possible solutions in that 3 digit range.

How would you accomplish that?

1. Loop over each number in the range of interest.

2. Extract the decimal digits.

3. Test to see if they satisfy the requirement.

Break a problem down into simpler sub-problems. Solve each one. Put it all together.

[edward wiltz]

Thanks John

[John D'Errico]

Note that the scheme I outlined is actually simpler than writing three nested loops, but it forces you to perform the step to extract the digits from a 3 digit number. There are always multiple ways to solve a problem. Your choice, since it is your homework.

Answer 1

[Matt J]

Here's a further hint.

>> num2str(347)-'0'

ans =

       3     4     7

[JR]

is it possible to do this problem without the code num2str( )

[Walter Roberson]

is it possible to do this problem without the code num2str( )

Yes! There is no need for num2str() at all if you use nested loops or a vectorized solution.

[Steven Lord]

Sure. One straightforward way would be to use three nested for loops as John D'Errico mentioned in this comment above. There are other ways, at the expense of higher memory usage, to avoid both num2str and for loops.

Answer 2

[Erass Mirza]

for numb = 100:999
    numb = num2str(numb)-'0';
    if numb(1)*numb(2)*numb(3) == 6*(numb(1)+numb(2)+numb(3))
       numb;
       x = str2num(char(numb+'0'))
    end
end

[Sudeepta Banerjee]

please can anyone explain me this answer ?

[Walter Roberson]

num2str of an integer returns a character vector in which the characters are the characters that encode the decimal digits of the value of the integer.

For example num2str of the integer forty-two finds the decimal representation 42 and then returns a vector of characters ['4' '2'] more commonly displayed as '42'

The character '4' is not encoded as the decimal value 4 in any system designed in the last 70 years. It might have been encoded that way in the 5-bit BAUDOT system long ago, which used the same codes for digits and letters and used a "Shift-in" and "Shift-out" code to tell you which range was active. So it might have happened historically, but long ago. And on the systems that did that historically, the digit 0 was encoded as binary ten not as binary zero because binary zero was mostly reserved for "line is idle"

In all systems since that long-ago BAUDOT, the characters to code the digits have not happened to be at the binary values that correspond to their decimal representation, because all of the systems reserved the low binary values as control characters, like idle or carriage return.

Instead, the characters for the decimal digits were, in all systems, allocated a block with the code for '2' always being immediately after the code for '1', and the code for '3' always being immediately after the code for '2' and so on. IBM had an economically important character encoding in which the code for '0' was immediately after the code for '9'.

In the mid to late 1950s, standards bodies formed and standardized on the current practice of encoding '0' then '1' then '2' and so on all as consecutive codes.

When you know that the characters for the digits are consecutive, then it becomes trivial to convert from the character representing a decimal digit, into the equivalent binary value of the decimal digit: just subtract the character code for '0' from the character code for the decimal digit and you get the binary. '4'-'0' subtracts the encoding of character '0' from the encoding of the character '4' and gets binary 4 as the result. It does not matter where in the encoding table that '0' through '9' occur, as long as you know that they are in sequence.

It is very useful to have '0' to '9' be consecutive characters, so it is unlikely that this property of character encoding of digits will change as long as we continue to use decimal. If we eventually switch to base 12 or 20 or 60 as some people have proposed, then the matter would be revisited. (The proposals for base 60 have been serious. Base 60 allows direct lossless encoding of 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/20, 1/30)