You have 3 slots. You MUST fill each slot with one number. Each slot has list of possible numbers. Find best combination(s) that have total sum equal or closest to curtain limit.

fill_buckets.coffee

_ = require 'underscore'

class BlackMagic
  dp: null
  dpMax: null

  maxTotalWeight: 0
  minTotalWeight: 0
  minWeight: Number.MAX_VALUE

  constructor: (@items) ->
    @bucketsNum = @items.length

  _setProperties: ->
    for bi in [0...@bucketsNum]
      weights = _.map @items[bi], (obj) -> obj.weight
      min = _.min weights
      @maxTotalWeight += _.max weights
      @minTotalWeight += min
      @minWeight = Math.min @minWeight, min
    console.log """
    maxTotalWeight: #{@maxTotalWeight}
    minTotalWeight: #{@minTotalWeight}
    minWeight: #{@minWeight}
    """

  _calcDPTable: ->
    @_setProperties()
    @dp = []
    @dpMax = []
    for bi in [0...@bucketsNum]
      @dp.push []
      @dpMax.push []
      for j in [@minWeight..@maxTotalWeight]
#        console.log bi, j
        rowMax = [-Number.MAX_VALUE, []] #Max value, and all ITEM ids have it
        for id, {value, weight} of @items[bi]
          @dp[bi][j] = [] unless @dp[bi][j]
          nextValue =
            if bi is 0
              if weight <= j
                value
              else
                0
            else
              if (j - weight) < @minWeight or @dpMax[bi - 1][j - weight][0] is 0
                0
              else
                value + @dpMax[bi - 1][j - weight][0]
          @dp[bi][j].push nextValue

          if nextValue > rowMax[0]
            rowMax[0] = nextValue
            if nextValue > 0
              rowMax[1] = [id]
            else
              rowMax[1] = []
          else if nextValue is rowMax[0] and nextValue > 0
              rowMax[1].push id

        @dpMax[bi][j] = [Math.max(rowMax[0], 0), rowMax[1]]

  print: ->
    for j in [@minWeight..@maxTotalWeight]
      row =
        for bi in [0...items.length]
          ' [' + @dpMax[bi][j][1].join(',') + ']' + @dpMax[bi][j][0]
      console.log j + ':\t' + row.join '\t\t'

    for j in [@minWeight..@maxTotalWeight]
      row =
        for bi in [0...items.length]
#          console.log(@dp[bi][j-@minWeight])
          @dp[bi][j]?.join('\t') + '[' + @dpMax[bi][j][0] + ']'

      console.log j + ':\t' + row.join '\t'

  findSolutions: (limit, howManyMax=10) ->
    @_calcDPTable() unless @dp
    if limit < @minTotalWeight
      throw "No solution"
#    @print()
    solutions = for i in [1..howManyMax]
      w = if limit > @maxTotalWeight then @maxTotalWeight else limit
      ids = for bi in [@dpMax.length - 1..0]
        _ids = @dpMax[bi][w][1]
        id = _ids[Math.floor(Math.random() * _ids.length)] + ""
        w -= @items[bi][id].weight
        id
      ids.reverse()
    _.uniq solutions, (item) -> item.join('')


items = [
  {
    0: value: 1, weight: 1
    1: value: 2, weight: 2
  }
  {
    2: value: 2, weight: 2
    3: value: 4, weight: 4
  }
  {
    4: value: 3, weight: 3
    5: value: 1, weight: 1
    6: value: 5, weight: 5
  }
]

items =
  for i in [0...3]
    obj = {}
    for j in [i * 100...i * 100 + 100]
      value = 100 + Math.floor(Math.random() * 99) + 1
      obj[j] =
        value: value, weight: value
    obj

bw = new BlackMagic(items)

console.log bw.findSolutions(400)
#console.log bw.findSolution(11)