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This is a problem that is prominently featured in the film Die Hard With a Vengeance.

You have a 3-gallon and a 5-gallon jug that you can fill from a fountain of water.

The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?

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'All will be well if you use your mind for your decisions, and mind only your decisions.' Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.

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Answer to the water jug riddle

The first attempt people have is to try and estimate 4 gallons by adding 3 gallons of water to 1/3 of the 3 gallon jug. But the riddle is asking for a precise measurement and so this solution cannot work.

The trick is to realize that:

5 – 3 = 2
and
5 – (3 – 2) = 4

Here is one way to find the answer:

That’s not the only path. We can also consider the route:

Incidentally, the reason we can find a solution is because the two numbers 5 and 3 are relatively prime–that is, they have no common divisors. We can actually generate any volume of water from 1 to 5 (in fact, we did get measurements of 1, 2, 3, 4, and 5 along the way in our solutions).

The more general problem is finding integer solutions for the equation ax + by = c. Solutions (x,y) exist when the greatest common divisor of a and b is a factor of c. This is an ancient problem. For more, read this article: http://mathforum.org/library/drmath/view/51595.html
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(This is the solution in plain text)

1. Fill up the 5-gallon jug
2. Fill up the 3-gallon jug using the water from the 5-gallon jug (leaving 2 gallons in the 5-gallon jug)
3. Pour out the 3-gallon jug into the fountain
4. Transfer the 2 gallons from the 5-gallon jug into the 3-gallon jug
5. Fill up the 5-gallon jug
6. Transfer water from the 5-gallon jug until the 3-gallon jug is full. Since the 3-gallon jug already had 2 gallons of water, there is room for just 1 gallon.
7. The amount of water in the 5-gallon jug is precisely 4 gallons

If we denote the contents of the jugs as the pair (5-gallon jug amount, 3-gallon jug amount), the sequence of events is:

(5, 0)–>(2, 3)–>(2, 0)–>(0, 2)–>(5, 2)–>(4, 3)

That’s not the only path. We can also consider the route:

1. Fill up the 3-gallon jug
2. Transfer to the 5-gallon jug
3. Fill up the 3-gallon jug again
4. Transfer water to fill up the 5-gallon jug, leaving 1 gallon in the 3-gallon jug
5. Empty out the 5-gallon jug
6. Transfer the 1 gallon to the 5-gallon jug
7. Fill up the 3-gallon jug and transfer that to the 5-gallon jug
8. The 5-gallon jug contains 4 gallons of water

The sequence here is:

(0, 3)–>(3, 0)–>(3, 3)–>(5, 1)–>(0, 1)–>(1, 0)–>(1, 3)–>(4,0)

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1. Die Hard: Nakatomi Plaza

Description of Die Hard: Nakatomi Plaza Windows

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Die Hard: Nakatomi Plaza sucks. All that follows is exposition thereon.

For those still interested, the game is based on the first film of the Die Hard series, in which cunning Alan Rickman takes over the state-of-the-art Nakatomi Plaza building as part of a deeply devious robbery, and only Bruce Willis, there to meet his separated executive wife, can stop the faux terrorists. It's a great action flick noted for a stonking villain, displays of ingenuity on both sides, pulse-pounding set pieces and an all-too human hero who gets hurt and tired and frustrated rather than simply displaying the traditional action-hero square chin and invulnerability. Sadly, all these points are missing from the game.

Looks and Sounds

Die Hard: Nakatomi Plaza is a first-person shooter using the versatile Lithtech engine, backbone of such fine offerings as No-One Lives Forever and Alien vs. Predator 2. Here, though, little is done with it. Detail is low, animation poor, characters blocky - in the wake of Return to Castle Wolfenstein and Medal of Honor, Die Hard looks crude. It doesn't help that the entire game is set in an office block, which means the environments are limited to plush offices, not-so-plush offices, offices-that-aren't-finished-yet, sewers (because it's not an FPS without them), a laboratory, a roof and a parking lot. What's more, the Nakatomi interior designers favour the ever-so-interesting colours of white, grey and beige, making these environments both boring and repetitive, and the trick the game pulls later on, of making you blunder around levels in the dark doesn't spice things up any.

If a game is going to be based around a restricted environment, something else needs to take up the slack. There must be action to keep up the pace and tight plotting to keep you guessing. Half-Life, one of the best shooters ever, is set entirely in a very functional research base and yet works brilliantly. Die Hard: Nakatomi Plaza doesn't.

Characters are poor, too, with jerky animation and low polygon counts. Sierra apparently don't have the rights to use the likenesses of Bruce Willis or Alan Rickman, and to prevent glimpses of Mr Willis, the game is careful to exclude him from cutscenes and restrict itself to first-person view when he would be present in a shot. To make entirely sure the copyright on Bruce's face is sacrosanct, the mirrors in the bathrooms don't reflect, which is a bit of a surprise in this day and age.

When fire, destroyer of cities and bane of civilisation, is called upon to play a role, it is here acted by disastrously animated wibbly-wobbly orange stuff. It looks stupid, and rather fails to inspire the terror that a blazing inferno in a confined space ought.

The sound is fine. Guns go budda-budda, bad guys shout things from a rather limited selection in German-ish accents and fire crackles. The context-driven music is okay, but nothing exceptionally notable or unworthy.

However, not since the otherwise spiffy No-One Lives Forever has a game suffered from such dull, turgid, drawn-out interruptions to game play. All are displayed using the game's uninspired graphics, in which ridiculously polygonal characters open and close their mouths in bland mid-distance shots while dialogue is played. It's often difficult to work out what's actually going on in them, and who's meant to be who. None of the film's tension is carried over to the cutscenes, which, instead of advancing the plot, suck away any glimmerings of tension as effectively as the very voids of space itself.

Story and Mission

Die Hard: Nakatomi Plaza bases itself on the film with near-fanaticism. Assuming you've seen the film (and surely everyone has) you'll know all the plot twists and all the set-pieces, which neatly excludes one reason to play all the way through. Sometimes you'll need to rely on knowledge of the film to progress: unless you remember that at one point McClane used a fire hose to jump off a roof, you'll spend a frustrating period running around trying to work out what the hell you're meant to be doing while dying over and over again.

In order to pad things out, a few new events have been added, which are a mixed bag. There's a nice section down in the parking lot escorting Argyle to a safe place, a section helping a SWAT team, and a Towering Inferno moment when you have to guide a hostage through a level as fire spreads, which would have been a lot more fun if aforementioned hostage wasn't so cripplingly stupid. The new sewers and labs, however, are dull. There's also a suspension of disbelief issue brought about by the conventions of FPS games. Instead of Hans Gruber and his hand-picked team of ten or so terrorists, we have Hans Gruber and his hand-picked team of two or three hundred terrorists... at one point John tells officer Powell over the radio that the terrorists are down by one, despite the fact you've gunned your way through about thirty of them by that point.

The game also suffers from obscure mission objectives. Generally, the only way to tell what you're meant to be doing at any one time is to press the 'O' key to bring up a list - rarely does the game content give you any guidance. Even the listed objectives are often unhelpful and apparently random ('Jump off the roof' being my particular favourite - I did. I died.).

Gameplay

Die Hard: Nakatomi Plaza attempts to add a couple of minor innovations to the standard FPS setup, but both end up being rather pointless. As well as a health bar you have to account for stamina and morale. Your stamina falls as John runs, jumps and otherwise exerts himself, and once depleted he can't do any of that stuff anymore. Unfortunately, stamina hardly ever comes into play during shootouts, where exertion consists mostly of leaning slowly from behind a wall, and instead kicks in when you have cleared the level but are running around looking for the way out. Its main function, then, is to slow down gameplay. The morale bar drops as you take damage and find yourself in dire straits, and has no perceivable effect whatsoever. Compliments, though, on the complete absence of jumping puzzles, which are never a good idea in games that don't let you see your feet.

Cheat Code For Die Hard 5 Java Game

Enemies have fairly basic AI which lets them lean around corners and otherwise make decent use of cover, and sometimes roll across the floor to thwart your aim, but they don't co-operate in any perceptible way and have a tendency to stand there firing blankly as you charge towards them. There's a modest selection of weapons available: a pistol, an MP5, an M16, a sniper rifle, a heavy machine gun and flash grenades. You'll use the MP5 to the near-exclusion of all else, because ammo for it is plentiful while being scarce for the other weapons.

There are a few unforgivably maddening moments. Certain scripted events, like a firefight between the terrorists and SWAT team, would be much more effective if it did something to hide the fact that the terrorists are invincible (found out by sniping 35 rounds into the head of one of them). Progress cannot be made unless you follow a specific course through the level, then amusingly witness the last of the untouchable terrorists go down just as you round a corner. While I'm a fan of cinematic moments in games, they should blend with the surrounding action (cf. Half-Life), and not be clumsily and restrictively imposed on the gamer.

Oh, and the dramatic final confrontation with the hostage-holding Gruber is rendered somewhat farcical when Gruber's apparently iron-skulled head allows him to withstand multiple high-velocity rounds with barely an 'ouch'. At one point it's possible to wander round behind Hans and shoot him in the back without fear of hitting Holly. The game couldn't handle such underhanded tactics, though, as Hans left Holly, who continued to act as if being strangled, and backed off towards the window, still acting as though he had a hostage. I emptied a few dozen rounds of ammo into him, but he didn't seem to mind.

Conclusion

Die Hard: Nakatomi Plaza is likely to appeal only to FPS fans desperate for a fix. The game is well behind its peers in execution and presentation, and fails to do anything interesting with the Die Hard license. In its favour, it should be retailing at a cheap and cheerful £19.99, which is a move towards reasonability for a game with no multiplayer support that will take shy of ten hours to play through to the end. On the whole, an eminently forgettable title that will do nothing for the reputation of film tie-in games.

Review By GamesDomain

External links

Captures and Snapshots

Screenshots from MobyGames.com

Comments and reviews

Wraithchylde2020-08-260 point

Can't get the game to start, have the original disc, and even tried the download here, patched, and cracked, will not start. Any ideas?

GoldenWolfe2020-07-25-1 point

Eh its repeditive and terrible

Blackheart2020-05-030 point

Im using win 7 64bit.... even i mount it in power iso its still looking for the CD

Durukan2020-04-160 point

Now i have a machine gun! HO HO HOO :)

Clyde3D2020-04-010 point

There is an 'improvement' mod for this game at moddb!
copy and paste this into your browser:
https://www.moddb.com/mods/die-hard-improved-edition

Bruce Willis2019-11-20-2 points

I'm Bruce and I loved killing innocent people in this game.

Camo2019-08-181 point

RETRO_SWEDE Run it in Windows 10 by mounting the img in File Exporer.

retro_swede2019-08-131 point

I am not sure how to get this game running. An .img file is included in the download folder. I opened it up on an old windows xp computer and ran it using magicDisc to run it as a virtual disc and I installed the game. I can get the start dialog running with autorun.exe and I click play but then nothing happens. any tips?

Bob2019-01-190 point

Nice homage to the film. Not a bad game.

vong2019-01-101 point

Goooood, Willis.

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