Halloween is just around the corner and the witch is planning a little party for the 100 villagers of the nearby village. Since the villagers burned down her house again and again during the last few years she would like to use this chance to make peace with them.
At least that is what she told the villagers.
Of course an evil witch would not simply forgive being attacked and so she collected the essences of animals, to be exact the essences of bears, hawks, and spiders, during the past year. Her plan is to use these essences to concoct potions which would transform the drinker into a creature with characteristics of all 3 animals.
Of course there are rules for these potions:
- The witch must concoct each potion on its own so 100 potions in total.
- For the concocting process all 3 essences are needed in a specific order, therefore each potion must contain at least a small amount of each essence.
- Each potion must must be concocted of the same amount of combined essences to get potions of equal strength. Otherwise the villagers who drank a stronger potion would be able to cancel the transformation of those who drank weaker potions.
- So the villagers would never find happiness again no two villagers should have the same transformation. Therefore each potion needs to be concocted using a different combination of amounts of essences.
Especially her last rule is a big problem for the witch.
She is only in posession of 4 magical cauldrons. One to contain each essence and one to concoct potions.
Unless the essences are in a complete potion or in one of the cauldrons they will dissipate in a matter of seconds so the witch can't measure the amount of essences for each potion beforehand.
Furthermore the concocting process is extremely complex and if she doesn't constantly stir it the incomplete potion would explode in her face.
For these reasons she can only use one ladle per essence to measure the needed amount for a potion.
How many different sized ladles does the witch need to concoct all 100 potions?