An Indian board commuinty questioned their students. No body answered but one of them.

The Question is simple: _+_+_=30

Numbers to be used:" 1, 3, 5, 7, 9, 11, 13, 15 " only (Odd numbers upto 15)

You can use same number twice & can't put '0' anywhere in blanks.

Anyone out there to help?

Guest Apr 22, 2015

#1**+10 **

If you add 3 odd numbers the answer cannot be even. Therefore they cannot add up to 30

Melody
Apr 22, 2015

#2**+8 **# A: 1_{(5) }+ 11_{(5) } + 13_{(5}) = 30_{(5)}

** â™š â™š â™š â™š â™š â™š **

Q: The Question is simple: _ + _ + _ = 30

Badinage
Apr 22, 2015

#3**+5 **

Nice try Badinage, but the question specifies *odd* numbers and 11_{5} and 13_{5} are even numbers!

.

Alan
Apr 22, 2015

#4**+5 **

The comment "(Odd numbers upto 15)" looks like the poster's interpretation designed to mislead, rather than part of the problem specification. That's what I'm claiming!!

Badinage
Apr 22, 2015

#5**+5 **

But the number 15 is specified and there is no 15_{5}.

I like your lateral thinking though! Try it with numbers to the base 7 (make sure the they are all odd).

.

Alan
Apr 22, 2015

#6**+5 **

There is significant ambiguity here (admittedly, that's what often makes math puzzles interesting!).

"Numbers to be used: ..." could be interpreted as ALL of these (sequences of digits) must be used at least once,

but then adding

"only" carries an implication that the solution is exclusive to those within that given sequence, and not that they all necessarily be utilised.

Also, it is not clear if the solution can include functions such as log_{n} or power^(1/n)

So, possibly there is a whole raft of solutions, limited only by ones imagination.

Badinage
Apr 22, 2015

#7**+5 **

Hi Alan and Badinage

So Badinage, if there is a 'whole raft of solutions' are you going to give us one of them that Alan won't poke holes in ? LOL

Melody
Apr 23, 2015

#9**+10 **

Best Answer**1357911 mod 13 + 111315 mod 13 + 13571 mod 13 = 30**

** ðŸ˜¡ ðŸ˜¡ ðŸ˜¡ ðŸ˜¡ ðŸ˜¡**

**It would be interesting to know exactly what the examiners had in mind. A lot hinges on what is meant by "using the numbers".**

**if we can use mod, here is one of infinite possibilities:**

Badinage
Apr 26, 2015

#10**0 ****$${\mathtt{1\,357\,911}} \,{mod}\, {\mathtt{13}}{\mathtt{\,\small\textbf+\,}}{\mathtt{111\,315}} \,{mod}\, {\mathtt{13}}{\mathtt{\,\small\textbf+\,}}{\mathtt{13\,571}} \,{mod}\, {\mathtt{13}} = {\mathtt{30}}$$**

Thanks Badinage :))

**BUT** only odd numbers up to 15 were supposed to be used

Melody
Apr 26, 2015