Hydra Slayer (now at v18.0) semi-$

[getter77]

http://zenorogue.blogspot.com/
http://www.roguetemple.com/z/hydra/
https://zenorogue.itch.io/hydra-slayer
http://store.steampowered.com/app/432380  $5.99 Win/Mac/Linux

You are facing a nine-headed hydra. Your flaming longsword cuts five heads in each swipe (no more, no less), which will kill a five-headed hydra, but a larger one will regrow two heads after each swipe. Your storm scythe cuts exactly seven heads, but it makes ten heads grow back if the hydra is not dead. Is it possible to kill the hydra? What if you also had a silver dagger, which cuts just one head, but makes five heads grow back?

Solution: It is impossible without the silver dagger (the number of heads always stays divisible by 3), but possible with the silver dagger, for example: 9 -> longsword -> 6 -> longsword -> 3 -> dagger -> 7 -> scythe -> 0.

If you liked this puzzle, and you also like dungeon crawling, Hydra Slayer is for you!

Hydra Slayer is a roguelike (randomly generated dungeon crawler), with unique combat mechanics based on the puzzle above. It is challenging both at a short term tactical level (each hydra is a unique challenge, bumping into it with your weapon almost never works), and at a long term strategy level (you have to build a set of weapons which slays hydras effectively). While the early levels could be used to teach arithmetics and tactical planning in a fun way, building an effective set of weapons for late levels is a challenge even for expert number theorists!

Hydra Slayer currently features a tutorial, 5 player character races with distinct characteristics, 28 enemy types (10 common hydras, each in two varieties, and 8 special enemies), 28 types of equipment including rare artifact weapons with special properties (not counting material and size variations), 15 weapon materials, 18 types of magical items which help you in your quests, three game geometries to choose from, 8 level topologies on very deep levels (including the Möbius strip and Klein bottle), 11 level generators, and two endings (a small victory for quick challenges and more casual players, and a big victory for those who want more challenge).

Hydra Slayer is available for free from its website. By buying the Steam version, you get typical Steam features, and more frequent updates -- currently, the Steam version has the following bonus features:
online achievements and leaderboards
Steam trading cards
cloud-based saves
daily challenge
automatic updates
a "challenge" mode for short but very interesting games (much more unpredictable than the normal play)
updated interface and performance (watch those heads fly!)
new music
traps to lead hydras on
Orbs which provide a powder/potion effect many times at the cost of a weapon slot
source code (except the Steam features)

v18.0   

The highlights of release 18.0 are the following:
A new player race, the Atlanteans. Most characters in Hydra Slayer would meet vulture hydras, who grow one head for every wound they deal to the player. The Atlanteans have been cursed by the gods, and this will happen for all hydras. Will you be able to turn your curse into an advantage? The curse significantly affects the equipment and strategies to use, especially in the first 12 levels. Thanks for Patashu and Nick for the idea!

Evolving hydras. They start to appear after level 25. Their resistance to the given weapon material is increased by one after each attack. These are inspired by a (slightly trollish) post by IchigoMait.

Previously, each level below Level 12 contained just one special hydra (not counting bloody or dragon variants of standard colors) -- since there are 9 types, some of them will appear just a few times. The new version changes this -- some levels will replace one of the standard ones with another special, and some will almost lack normal hydras and include most of the special types instead. Challenge levels now tend to have two special hydras per level too.

One new exotic weapon -- I will leave that for the players to find
New special graphics for scythes (Atlanteans start with a scythe), hecatoncheires and monkeys. Thanks to tehora for requesting these!

Removed some exploits. It is no longer possible to enhance the titanic club easily with the Reforging+Ambidexterity combo (thanks to vo3435 for abusing this). A tighter limit is placed on using time-daggers on mushrooms.
Some features have been added to help with "head draining" attacks (all hydras for Atlanteans, Vultures for all characters). When fighting head-draining hydras, the number of wounds caused by the hydra's next attack is given in the UI. For other hydras, when you select your shield, "+1" is displayed for the hydra whose damage is reduced by your shield. Also, you can now press 'w' in the hydra description, to view the amount of wounds the given hydra would deal for every size. Enchanted Mersenne Twister (when trying to roll a 'good' number of heads) will now take into account that extra heads could be drained.
In the cheat mode, shift+H can now also summon equipment.

Minor bugfixes: better display of the in-game achievement screen, capital letters accepted in the scores menu, better handling of the app going out of focus, the generation of Giants' weapons in challenge games, crash bug with Vulture + Ambidexterity + Knowledge/Growth, using Twister even though runes are active, inexact calculation of wounds in the PoK algorithm by head drainers, 'use count' for traps, dragons attacking in a wrong direction on non-orientable levels, number of stunned heads is no longer displayed in the PoK hint for large hydras (the algorithm does not care about them anyway), potion of knowledge correctly counting wounds for shadows, capital letters accepted in the scores menu