tuesday puzzle

Now for one a bit more challenging

The question marks can be any digit from 0 to 9 and can be duplicates. Can you find the correct value for each one of them?

hint for easy one

the fact that I am looking for the next three is significant.

Re: Combination...

to Ft. Knox? What seems easy to some, is.........non understandable to others. I've lookd for arithmetic ways. Words: prime, ingerers, etc. Wait(!)......I've GOT IT! They are all whole numbers so the other three will be whole numbers, that gotta be correct!

Well, yes, but (another hint)

They are whole numbers, but which ones ;-)

Another hint. think Non harmonically related series.

Music to my ears

Chromatic scale is thirteen notes

Re: Music to my ears (another hint)

Don't think so, but explain a bit more. ;-)

Remember the first hint about looking for three numbers. That is important.

FWIW

I gave this problem to a math lab group that I assist with (high schoolers) and one of them came back the following week with the answer ;-) It looks intimidating, but if you remember how division works and the possibilities for various multiplications, it comes out with just a bit of work. The attached picture is one I posted here quite some time ago and is an easier version of the above. In this case, each letter is unique, no dups.

I was thinking

frequencies. I don't connect any integer sequence. As it is frequencies don't match up either. Letters to numbers don't work neither does spelling of the numbers. Atomic weights don't work out. I cannot think of any thirteen number scale/sequence except the tone music scale. Gray scales and f-stops don't work. Wind scale and color charts don't seem to work. I'm thinking transposition of letters and numbers as in code (but the 27 screws it up). Thirteen numbers in a ____? Thirteen weeks in a season. Thus far you're winning.

remember that I asked for three numbers.

The fact that I am asking for 3 numbers is very important. When I say not harmonically related, I mean that they are not direct multiples. Think again about the three. There are several things going on here. (another hint)

BTW, 13 has nothing to do with it.

Start with H*(200+10H+5)=100T+10H+P

As long as you have as many equations as you do variables, it's just grunt work after that...

Steven

Who theoretically could have done this in his head 25 years ago...

Re: Start with H*(200+10H+5)=100T+10H+P

You can also do it just using the rules of multiplication, subtraction and division. The other one that I posted does not lend itself very well to the simultaneous equation method ;-)

and still another hint;-)

Think 5, 7, and 11

Answer to the easy one

There are three intertwined series, going up by 5, 7, and 11. (non-harmonic terms;-))

Take the first three numbers, add 5 to the first write it down, then 7 to the second, write it down, then 11 to the third. Repeat with the three numbers that you just formed.

The answer is 24, 38, 22