# Convert 3 numbers to 1 with a hidden rule

I have a secret rule that converts 3 numbers into one via a strange function. I've run 10 sets of numbers through my rule and recorded the results here.

• 2-1-3 = 5
• 4-1-2 = 6
• 2-4-3 = 16
• 4-2-3 = 12
• 5-2-1 = 5
• 3-2-2 = 6
• 2-3-3 = 8
• 4-3-2 = 16
• 5-1-3 = 8
• 2-4-2 = 4

The puzzle here is to figure out what the rule is. If you think you've figured out the rule, tell me what number is produced by each of these sets of numbers.

• 5-3-2
• 3-4-3
• 3-1-6
• 6-2-4

The only other hint I think you'll need is this: one of answers I'm looking for is a 13 digit number.

• Couple of questions: Does the order of the numbers matter? Or you can feed the numbers into the function in any sequence. Second, is the '-' sign an operator or have you used it to separate the three numbers? For example, is the first solution 2 (some operator) 1 (same operator) 4 = 5? Apr 11, 2018 at 4:58
• The order of the numbers in each set is very important. The "-" is just a divider. Apr 11, 2018 at 4:58

Easy. I'm surprised nobody got it yet.

25
7,625,597,484,987
9
24

Hyperoperation: https://en.wikipedia.org/wiki/Hyperoperation.
Given 3 numbers, a-b-c, the answer is Hb(a, c).

• No need to add this is easy. Like many many puzzles here, it is easy for those who know what it is about or have already met a puzzle of the same kind, and it is hard for the others. Welcome to puzzling.SE btw! Apr 11, 2018 at 8:55
• It also helps to discover the puzzle at a local time when coffee is an option :) Apr 11, 2018 at 11:04

I found something slightly different and way more trivial that match everything, except for the last hint.

Each line is composed of n-a-m. n and m are the variables, a is the operator :
1 means n+m
2 means n*m
3 means multiplyn n by itself m times
4 means n^m

That gives us

5-3-2 -> multiply 5 by itseld 2 times -> $5*5 = 25$
3-4-3 -> $3^3 = 27$
3-1-6 -> $3+6 = 9$
6-2-4 -> $6*4 = 24$

• The only difference between your answer and hyperoperation is for a=4. According to your rule 2-4-3 would yield 8, not 16. And I don't see the difference between a=3 and a=4 (multiplying n by itself m times means n^m, right?) Apr 11, 2018 at 9:00
• Oh yeah you're right, i derped out on this one Apr 11, 2018 at 13:23