# If $5 * 5$ = $10$ , $6*6$ = $18$ , $7*7$ = $36$ ; then $7* 8$ =? [closed]

If $$\quad 5 * 5 = 10$$ ,
$$\quad 6*6=18$$
$$\quad 7*7=36$$
then $$\quad 7* 8 = ?$$

a) $$54 \quad$$ b) $$51 \quad$$ c) $$30$$

NOTE: Here '$$*$$' is not simple multiplication
It is some logic or combinations of operations from which we are getting $$10$$ from $$5$$ and $$5$$
Similarly, we are getting the rest of the relations via the same logic or combinations of operations

My Thoughts:
$$10= 5*(5-3)$$ i.e, LOGIC: $$\quad x* (x-3) =$$ RHS
Similarly $$2nd$$ relation is satisfied, i.e, $$18=6*(6-3)$$ $$\text{But, } 36 \neq 7 * (7-3)$$ So, how to solve this puzzle? Any Suggestions please...

## closed as off-topic by Saad, Rhys Steele, Riccardo.Alestra, Vinyl_cape_jawa, Xander HendersonMar 7 at 13:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is not about mathematics, within the scope defined in the help center." – Saad, Rhys Steele, Riccardo.Alestra, Vinyl_cape_jawa, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.

• All of 3 can be correct. – Botond Feb 26 at 8:10
• How? Can you please explain... – Suresh Feb 26 at 10:09
• The $*$ function is not well defined, so $7*8$ can be anything. – Botond Feb 26 at 11:25
• "$*$ is not well defined" , I agreed; but in this problem that is what required to be find. For eg.: '$*$' should be defined in such a way that it satisfies given $3$ relations, and then that definition of '$*$' should be used to evaluate $7*8$ – Suresh Feb 26 at 13:33
• But you can't give an unique extension with the given conditions. You can let, for example $5*5=10, 6*6=18,7*7=36$ and $0$ otherwise. Why would any other extension be better or worse than this one? – Botond Feb 26 at 14:10

Suggestion: Let $$ab=10x+y$$. Then $$a*b=f(x,y)$$.
• Sorry i could not understand, could you please explain how we can relate $10x + y \,$ with $5*5=10$ ? – Suresh Feb 27 at 6:20