How fast can you solve this tricky puzzle?

[pattersonpaul]

The world record for solving this tricky puzzle is 13 seconds
It took my 40 minutes to solve

[kb83]

I got an answer, based on non-decimal-based arithmetic, and a descending progression of bases.

[hrossa]

Maybe don't click PattersonPaul's link. I did, but got a warning from my antivirus software.
Spoiler alert, my solution is in the next sentence.
You can find many different patterns for short series such as this. I got an answer in a couple of minutes using another pattern than kb83 (though I like yours better, kb83). Here's another pattern that works. By adding the previous sum from the line above to the two new addends in the current line, you get 40 in the last line.

[Fudi]

Spoiler alert here too: I came up with 52 as an answer in about a minute. I came up with it this way:

4x1 + 1 = 5
5x2 + 2 = 12
6x3 + 3 = 21
11x4 + 8 = 52

Dunno.

[hrossa]

Nice, Fudi, that's fun!

[kb83]

So let me better explain my solution.

In base 6, 1+4 = 5 (of course this is true in any base of 6 or higher)
In base 5, 2 + 5 = 12 (but of course the left side of the equation is not really written in base 5)
In base 4, 3 + 6 = 21
and in base 3, 8 + 11 = 201. So my answer was 201.

So a better way to say it is, my solution is the result of adding the 2 addends on the left (in base 10), and then converting the result to the next lower base in the progression.

[Fudi]

That's an interesting solution, kb. But beginning the pattern with base 6 seems kind of random to me. I dunno. To me, it seems more logical that the first equation would make use of the number 1, the 2nd equation would make use of the number 2, and so on. Just my humble opinion.

[hrossa]

^ This one is my favoriet, so far.

[portport]

I like hrossa's answer of just keeping the running total sum

[Anachronismatic]

The one I came up with was A + B really means A(B+1). Like Fudi's, but ends in 96. I'm sure there are plenty of others. Hrossa's has more elegance.

[hrossa]

Ooh, another good one. Really, they are all equally elegant (or inelegant) because all rely on an unseen rule behind the lines. It's fun how easy it is to find new ones.

[LLapp]

Just dropping in to say I'm glad there's a forum thread where the math people among us can mingle. And with that, I'm outta here.

[318WOZ]

Add 1 to the second number, then multiply it with the first.

[cryptoharvesting]

Fudi is correct, but if you can find other valid answers then they are also valid. Though Im inclined to think that the simpler the solution the better.

[Fudi]

Yes yes ... everybody's solution is right, of course, but mine is the *most* right!!! So cool! What do I win?? (Tee hee.)