The Heavy Pill Task. Solution in Swift

There are 20 bottles of pills. 19 bottles have pills of weight 1.0 gram, but one has pills of weight 1.1 grams. How to find heavy bottle? There is constraint: you can make only one measurement.

In order to find a bottle with heavy pills let's take 1 pill from a first bottle 2 from the second and so on up to 20. Also, we know in advance the total weight of pills in this calculation if in all bottles the pills weigh 1 gram. It will be 1 + 2 + 3 + ... + 20 = 210 grams. Thus, we need to deduct the summary weight of all normal pills from the summary weight of pills with heavy pills and divide by the difference between the weight of the heavy and normal pills(1.1 - 1 = 0.1 grams).

So, formula is

bottleNumber = (summaryWeightWithHeavy - summaryWeightNormal) / (diff)

where summaryWeightNormal = 210 grams, diff = 0.1 grams

bottleNumber = (summaryWeightWithHeavy - 210) / 0.1

Coding algorithm for checking solution and formula:

1. Generate random number for heavy bottle
2. In loop from 1 to number of bottles we calculate normal weight and "heavy" weight(when one of bottles has heavy pills)
3. According to our formula: We take the normal total weight from the heavy total weight and divide this difference by the difference between the weights for one pill
4. Check that found bottle number equals initial bottle number

Source code

import Foundation

let bottlesCount = 20
let normalPill = 1.0
let heavyPill = 1.1
let diff = heavyPill - normalPill

let heavyBottleNumber = 1 + Int(arc4random_uniform(UInt32(bottlesCount)))
print(heavyBottleNumber)

var normalWeight = 0.0
var heavyWeight = 0.0

for i in 1...bottlesCount {
    normalWeight += Double(i)
    if i == heavyBottleNumber {
        heavyWeight += (Double(i) * heavyPill)
    } else {
        heavyWeight += Double(i)
    }
}


let result = Int(round((heavyWeight - normalWeight) / diff))
print(result)
assert(heavyBottleNumber == result, "failed")