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I was about to try to join the famous Math club at my school when I stopped to hear my classmates doing the same. I didn't know that newcomers had to take a simple test to be qualified until my they tried it. It went like this:

Member : What is 1 * 3

Newcomer A : Is it 5?

Member : Correct, you may go in. B, what is 1 * 4 * 5?

Newcomer B : It's gotta be 14, right?

Member : Indeed, you may also go in. C, what is the result of 2 * 4 * 6 * 7 * 10?

Newcomer C : Is it 40?

Member : Wrong, but you are so close. Try again next time.

After hearing that conversation, I went to the member and said that I would like to join the club too. The member then asks, "Very well, tell me the result of 3 * 12 * 15 and if you are correct, then I will let you in."

What should I answer?

To clarify :

The symbol (*) does not mean to multiply.

Hint (Usefulness Level : 1) :

Observe the amount of numbers in the equations

Hint (Usefulness Level : 2) :

The pattern only uses 3 kinds of operations.

Hint (Usefulness Level : 3) :

Subtraction is not used in this pattern.

Additional Examples :

Member : What is 7 * 13

Newcomer D : Ummm...109?

Member : Well done! E, What is 2 * 2 * 4?

Newcomer E : I know the answer. It's 8 right?

Member : Yes, correct answer.

Extra Hints (As requested by @El-guest) :

1 * 4 = 8.5

4 * 5 = 20.5

2 * 4 = 10

2 * 2 = 4

Please show the pattern in your answer

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  • $\begingroup$ This riddle reminds me of this one. The link takes you to a puzzling site called Braingle. You can sign in if you want :) $\endgroup$
    – Mr Pie
    Commented Aug 13, 2018 at 9:33
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    $\begingroup$ OK. I'll check it out @user477343 $\endgroup$
    – Kevin L
    Commented Aug 13, 2018 at 12:13
  • $\begingroup$ @KevinL is it possible (would it help at all) to know the answers to say 1 * 4, 4 * 5, 2 * 4, or 2 * 2? $\endgroup$
    – El-Guest
    Commented Aug 13, 2018 at 15:12
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    $\begingroup$ You mean you want me to write the answers to those equations (extra hints) ? @El-Guest $\endgroup$
    – Kevin L
    Commented Aug 14, 2018 at 2:30
  • $\begingroup$ Thanks @KevinL! Unfortunately I went home for the night but glad they were useful! :) $\endgroup$
    – El-Guest
    Commented Aug 14, 2018 at 12:27

2 Answers 2

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The answer is

126

Square each value, add together, divide by numbers of values

(32 + 122 + 152) / 3 = (9 + 144 + 225) / 3 = (378) / 3 = 126

But the third clue seems to prohibit addition, so I'm not sure.
The third clue was changed to only prohibit subtraction.

Full list of equations: 

(12 + 32) / 2 = 5

(12 + 42 + 52) / 3 = 14

(22 + 42 + 62 + 72 + 102) / 5 = 41

(72 + 132) / 2 = 109

(22 + 22 + 42) / 3 = 8

(12 + 42) / 2 = 8.5

(42 + 52) / 2 = 20.5

(22 + 42) / 2 = 10

(22 + 22) / 2 = 4

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  • $\begingroup$ Wow, I didn't notice that I wrote addition was not used. Sorry I was very tired yesterday when I wrote the hints. BTW, correct answer @hagfy $\endgroup$
    – Kevin L
    Commented Aug 14, 2018 at 3:06
  • $\begingroup$ I searched for so long without using addition :( $\endgroup$
    – Marc Z
    Commented Aug 14, 2018 at 12:23
  • $\begingroup$ I'm very very sorry @MarcZ $\endgroup$
    – Kevin L
    Commented Aug 14, 2018 at 12:42
  • $\begingroup$ It's ok! No hard feelings $\endgroup$
    – Marc Z
    Commented Aug 14, 2018 at 12:50
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Just a guess (tried finding random patterns). Is it

42

Because

Amount of numbers * last number - first number
$2 * 3 - 1 = 5$
$3 * 5 - 1 = 14$
$5 * 10 - 2 =48$ (close to $40$), so
$3 * 15 - 3 = 42$

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  • $\begingroup$ +1 Nice try but no. Going to add another hint. Btw, what I meant by close was literally really really close --> 48 is not so close to 40. $\endgroup$
    – Kevin L
    Commented Aug 13, 2018 at 8:00
  • $\begingroup$ Yeah I guess that was sort of a stretch. $\endgroup$
    – sedrick
    Commented Aug 13, 2018 at 14:12

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