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https://github.com/oleksiyrudenko/12coins-3weighings


https://github.com/oleksiyrudenko/12coins-3weighings

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# 12 coins, 3 weighings



There are 12 coins. One is fake and its

weight is different from that of legit coins.



After 3 weighings tell which coin is fake.



## Installation



Run `npm install` or `yarn install` to install

required dependencies (Jest test framework).



Scripts:

- `yarn start` or `npm start` will run main algorithm tests

- `yarn dev` or `npm dev` will run `experimenting.js`

  supposed to use at algorithm development phase

- `yarn test` of `npm test` runs test of

  the built-in weight balancing helper



## The task



Your task is to write the code that would identify

the fake coin among 12 given.



Add some meat to `findFake` function in `./find-fake.js`.

The function parameters are:

* `array` - an array of coins weight, exactly 12 entries,

  all values are the same with exception for one which

  may be greater or lesser than others 

* `balance` - a function to weigh the coins



Your `findFake` function is expected to return an array of two

items where first item is a fake coin index in the 

input array and the second item is fake coin's weight/value.



So, `findFake([21,21,21,21,21,21,29,21,21,21,21,21], balanceMaker())`

would return `[6,29]` representing a fake coin where

`6` is an index of fake coin and `29` is its weight.



Use `balance` function inside your `findFake` 

to make weighings.

You may use your own balancing function but final tests will employ

the one provided by the author. It also calculates

number of its own invocations for you

(remember, 3 invocations is a maximum). 



The `balance` function takes 3 arguments that are:

- `array` - a source array representing 12 coins

- `set1indices` - indices of coins to put on the left plate

- `set2indices` - indices of coins to put on the right plate



The function returns `0` if the weight on both plates is equal,

a value lesser than `0`

if coins on the left are lighter, and a value greater than `0`

if coins on the left are heavier. 



For example `balance([2,5,2,2,2,2,2,2,2,2,2,2], [0,1], [7,8])`

would return `3` since `(2+5) - (2+2) == 3`, which means that

there is a heavier coin on the left plate.



Launch your experiments from `./experimenting.js`.

This module imports what is required and also

demonstrates a pattern of `findFake` invocation

using a balance function maker. 



Run `yarn dev` or `npm dev` to conduct your experiments. 



### Final tests



Once you feel done run `yarn start` or `npm start`

to have a complete test of your algorithm.



There gonna be 24 tests. All must pass for a good algorithm.



The only thing it cannot test is when you use your own

method of weighing that doesn't restrict the number

of weighings.



### Hints



Consider addressing to the hints below only after

a couple of attempts to solve the problem.  



Hint 1. Switch plates




Change of balance may help. So consider moving coins

between the plates. For example,

if `1 + 2 + 3 < 4 + 5 + 6` and `1 + 2 + 4 > 3 + 5`

then the fake coin is either `3` or `4` 'cause moving them

changes the balance.






Hint 2. Exclude




If `1 + 2 + 3 < 4 + 5 + 6` and `1 + 2 == 5 + 6`

then the fake coin is obviously either `3` or `4`.






Hint 3. Mix approaches




Employing both approaches above in a single weighing

can save you a weighing attempt.