# Just for fun: math brain teaser

• I
• whig4life
In summary, the conversation discusses different solutions to the equation a+b = a+a*b, with examples given for 1+1*4=5, 2+2*5=12, 3+3*6=21, and 8+8*11=96. The speaker mentions their friend getting 40 as a possible solution, but notes that there are infinitely many possibilities for constructing a building rule for this equation. They also mention other rules that could match, such as ##a \oplus b = ab+b-3## and ##a \oplus b = a^2+4a##. The conversation ends with a discussion about the solution of 40 and how it fits into the pattern established in
whig4life
TL;DR 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. I am not sure who is correct. Please let me know and let’s put our heads together and have fun.

I get ##201##

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

sysprog
fresh_42 said:
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?

whig4life said:
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.

whig4life said:
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.

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.

\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}

40
if
1 + 4 = 5
2 + 5 = 12 [12=5+2+5]
3 + 6 = 21 [21=12+3+6]
8 + 11 = 40 [40=21+8+11]

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