# Just for fun: math brain teaser!

• I
Summary:
Just for fun, let me know if I am a+b = a+a*b

1+1*4=5

2+2*5=12

3+3*6=21

8+8*11=96

my friend got 40, which I can also see. Im not sure who is correct. Please let me know and let’s put our heads together and have fun.

PeroK
Homework Helper
Gold Member
2020 Award
I get ##201##

fresh_42
Mentor
I had 96, too, but there is no unique solution. In fact, there are infinitely many possibilities to construct a building rule.

• sysprog
I had 96, too, but there is no unique solution. In fact, there are infinitely many possibilities to construct a building rule.

Hello my friend, and thanks for the reply. How did you arrive at 96, was it similar to my method?

fresh_42
Mentor
Hello my friend, and thanks for the reply. How did you arrive at 96, was it similar to my method?
It was exactly your approach. Appeared to be the easiest way.

Mark44
Mentor
Summary:: Just for fun, let me know if I am

a+b = a+a*b
That seems the most obvious solution, and one that matches the first three examples.

mfb
Mentor
Three other rules that match, using the common b-a=3 in all examples:
##a \oplus b = ab+b-3##
##a \oplus b = a^2+4a##
##a \oplus b = b^2-2b-3##

As the open problem has b-a=3, too, all these rules lead to 96.

pbuk
\begin{align} 1 + 4 &= 5_{10} = 5_6 \\ 2 + 5 &= 7_{10} = 12_5 \\ 3 + 6 &= 9_{10} = 21_4 \\ 8 + 11 &= 19_{10} = 201_3 \end{align}