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## Question

Prince Sindbad went to fight a 3-headed, 3-tailed dragon. He has a magic sword that can, in one stroke, chop off either one head, two heads, one tail, or two tails.

The dragon is of a type related to the hydra. If one head is chopped off, a new head grows. If one tail is chopped off, two new tails grow. If two tails are chopped off, one new head grows. If two heads are chopped off, nothing grows.

What is the smallest number of strokes required to chop off all heads and tails of the dragon, thus killing it?

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Nine.

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I am getting 9 as the answer as well. To get rid of everything you have to end up with an even number of heads and no tails left. To get an even number of heads with no tails left you need an odd number of pairs of tails. You can have 1 pair of tails or 3 pairs of tails. You already have more than one pair of tails because you have 3 tails so you must go to 3 pairs of tails. To get to this point it takes 3 strokes of one tail each thus doubling the tails to give 3 pairs of tails. Then chopping one pair of tails at a time converts these tails to heads so this takes another 3 strokes and results in 6 heads. Then chopping the heads off two at a time results in 3 more strokes and a dead dragon. This is the shortest way I found to do it.

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1: cut 2 tails, 1 new head comes up so now it has 4 head

2: chop the only tail left and 2 new tail comes up

3: cut the remaining 2 tail and now 1 head comes up so total head is 5 and no tail left

4: Cut 2 head and nothing comes up, so total head left is 3

5: Cut 2 more head and nothing comes up, so total head left is 1

6: Cut 1 more head and 2 head comes up comes up, so total head left is 2

7: Finally cut the remaining 2 head and the dragon is dead

So total stroked is 7

Edited by cool_dude
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Nine chops:

1t, 1t, 1t, 2t, 2t, 2t, 2h, 2h, 2h

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Nine total cuts.

Cut one tail off, three times in a row leaving you with six tails.

Then cut two tails off at a time, three times, adding 3 heads and eliminating all of the tails.

Finally, cut the six heads off in three cuts, two heads at a time.

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```

start               -111            111-

swing 1) 1T         -111            1111

swing 2) 2T         1111            -11-

swing 3) 2H         -11-            -11-

swing 4) 2H         ----            -11-

swing 5) 2T         ----            ----

because once you "chop off all heads and tails of the dragon, thus killing it" -- it's dead therefore the head from the two chopped tails doesn't grow

```

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```

start               -111            111-

swing 1) 1T         -111            1111

swing 2) 2T         1111            -11-

swing 3) 2H         -11-            -11-

swing 4) 2H         ----            -11-

swing 5) 2T         ----            ----

because once you "chop off all heads and tails of the dragon, thus killing it" -- it's dead therefore the head from the two chopped tails doesn't grow

```

While that sounds completely reasonable , I think the OP meant "dead" as "rendered in a position as of which no more heads/tails could spawn"

And I don't really think it can go below 9.

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While that sounds completely reasonable , I think the OP meant "dead" as "rendered in a position as of which no more heads/tails could spawn"

And I don't really think it can go below 9.

I agree

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Yes..no matter how many combination you try.it will take atleast 9 chances to kill the dragon completely..most people got it right

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