Question

A hero is fighting with a dragon.

At first, the dragon has three heads but each time the hero chops off a head the dragon grows three in its place.

How many heads does the dragon have after seven chops?

After $n$ chops?

Answer 1

Find the number of heads the dragon has after seven chops:

Step-1: To solve the initial head.

Initially, the dragon has three heads.

When the dragon has three heads but each time the hero chops off a head the dragon grows three in its place.

$3\times 3=9heads$

Now dragon has $9$ heads but already $3$ heads have been chopped.

The remaining heads that are chopped are,

$9-3=6\mathrm{heads}$

So the remaining heads haven't chopped is,

$9-4=5$

Step-2: Find the remaining heads of the dragon:

So now the dragon has four heads but each time the hero chops off a head the dragon grows three in its place

$4\times 3=12\mathrm{heads}$

So the remaining heads haven't been chopped is $12$

Now let us not count the chopped head.

The total number of heads is,

$12+5=17\mathrm{heads}$

As, after each chop, the number of heads would be an odd number.

When the first head is chopped and the dragon grows three in its place. So, the number of head would be $2+3=5$.

Now, after $n$ chops, the number of heads would be

$3+2n$.

Therefore, $\mathbf{17}\mathbf{}\mathbf{heads}$ does the dragon has after seven chops and after $n$ chops, the number of heads is $3+2n$.