How does this recursion work?

Question

This is an example from Eloquent Javascript:

By starting from the number 1 and repeatedly either adding 5 or multiplying by 3, an infinite amount of

Answer 1

goal is your objective and it's set to 24

goal == 24

Now we have this internal function find() that checks to see if start is equal to 24; its not. It also checks to see if start is greater then 24 this is also not true,

find(1 "1")
1 == 24 //false
1 > 24 //false

So it hits the else statement where it calls find again, this is where the null value from the else if() comes in. If the return is null then it calls the || part until it eventually finds the correct answer.

return find(6, "(1 + 5)")
       find(11, "((1 + 5) + 5)")
       find(16, "(((1 + 5) + 5) +5)")
       find(21, "((((1+5) + 5) + 5) +5)")
       //next one returns null!
       //tries * by 3 on 21, 16, and 11 all return null 

so it switches to the ||

return find(3, "(1 * 3)")
       find(8, "((1 * 3) +5)")
       //some calls down +5 path but that returns null
       find(24, "(((1 * 3) + 5) * 3)")

Finally! We have a true return and we have logged the path we took in the history var.