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How many possible types of wands can Ollivander make, if the variables are only core material, wood material, and length in inches?

This is a small subquestion related to this, and intended to establish a definite cap on how many maximum possible wands would a wizard be able to choose from (assuming, for any wizard, SOME wand will always choose him, with the choice determined by core material, wood material, and length)

Please note that the combinations are finite, based on Pottermore, since Ollivander does not use random materials.

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    Nah, they're infinite, if 12.12346 inches is different than 12.12345 inches. D'ya have a precision in mind? ;) – Izkata Oct 6 '12 at 4:14
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    I also would like some clarification on what defines a "type" in you opinion. I also don't think that core material, wood material, and length are the only contributing factors. For instance does the magical creature that the core material was obtained from make a difference? I'm not talking about whether it was a phoenix feather or something else... I'm talking about the fact that it makes a difference which phoenix it was obtained from. – Dason Oct 6 '12 at 4:20
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    This question does not deserve the downvote it received. It is actually one of the more precise and "objective without being obvious" Harry Potter questions on the site. – Gabe Willard Oct 6 '12 at 5:00
  • @Gabe. Seems there may be a persistent down-voter in action at the moment. It's been noted on some other questions as well - good questions with an anonymous (ie. gutless) down vote. – gef05 Oct 6 '12 at 6:16
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    Oh I'll DV without explaining it if I feel like explaining will only start an argument. I'm simply stating that this question isn't the quality that deserves a DV at all, despite it looking subjective. – Gabe Willard Oct 6 '12 at 6:45
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Fortunately for the sake of a reasonable answer, Ollivanders limits himself greatly as to which wands he will actually make. From Pottermore, articles on Wandlore:

Every single wand is unique and will depend for its character on the particular tree and magical creature from which it derives its materials. Moreover, each wand, from the moment it finds its ideal owner, will begin to learn from and teach its human partner. Therefore, the following must be seen as general notes on each of the wood types I like to work with best, and ought not to be taken to describe any individual wand.

...

Only a minority of trees can produce wand quality wood (just as a minority of humans can produce magic).

...

Most wands will be in the range of between nine and fourteen inches. While I have sold extremely short wands (eight inches and under) and very long wands (over fifteen inches), these are exceptionally rare.

...

Wand flexibility or rigidity denotes the degree of adaptability and willingness to change possessed by the wand-and-owner pair - although, again, this factor ought not to be considered separately from the wand wood, core and length, nor of the owner’s life experience and style of magic, all of which will combine to make the wand in question unique.

...

Early in my career, as I watched my wandmaker father wrestling with substandard wand core materials such as kelpie hair, I conceived the ambition to discover the finest cores and to work only with those when my time came to take over the family business. This I have done. After much experimentation and research, I concluded that only three substances produce wands of the quality to which I am happy to give the illustrious name of Ollivander: unicorn hair, dragon heartstring and phoenix feather.

Now, that limits it greatly. Ollivander sells wands made from thirty-eight different woods, listed here: Acacia, Alder, Applewood, Ash, Aspen, Beech, Blackthorn, Black Walnut, Cedar, Cherry, Chestnut, Cypress, Dogwood, Ebony, Elder, Elm, English Oak, Fir, Hawthorn, Hazel, Holly, Hornbeam, Larch, Laurel, Maple, Pear, Pine, Poplar, Red Oak, Redwood, Rowan, Silver lime, Spruce, Sycamore, Vine, Walnut, Willow, Yew.

Ollivander sells wands of three cores: phoenix feather, dragon heartstring, and unicorn tail hair.

Ollivander sells wands that are categorized as having one of eight distinct flexibilities: Unyielding, Hard, Rigid, Brittle, Reasonably Supple, Slightly Springy, Surprisingly Swishy, Quite Flexible.

The final variable is length. According to Pottermore, he cuts them off to precise quarter inches. Considering the vast majority of wands are between 9 and 14 inches long, that allows for twenty-one distinct quarter inch measurements between 9 inches and 14 inches.

By these statistics, we can deduce that there are a total of 19,152 (38 * 3 * 8 * 21) combinations of wand wood, core, rigidity, and length commonly made by Ollivander. He can certainly make other wands, but would not in common practice.


It is important to note that certain of these materials are exceedingly rare, such as Elder wood, and to a much lesser extent, Phoenix feathers. It is unlikely that Ollivander would keep a large quantity of these wands in stock, but they are still possibilities for him to make.

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    FWIW "Every single wand is unique and will depend for its character on the particular tree and magical creature from which it derives its materials" suggests that there may be additional magical variables involved. For instance if two wands were made with the same wood, length, and rigidity, but with phoenix-feather cores from two different phoenix, they would still be considered unique. E.g. perhaps one of the two would choose a particular wizard and the other would not. – David Z Oct 8 '12 at 21:22
  • @DavidZaslavsky The OP asked how many different "types" of wands can be made. That is a discrete number limited to 19,152. The article actually states that every wand is qualitatively unique when its components are factored with the user's personal casting style, however that is not a quantitative difference. – Gabe Willard Oct 8 '12 at 22:21
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    Of course, I never said otherwise. I just thought it would be worth mentioning that the calculation you did here to show that there are 19152 types of wands doesn't mean that Ollivander can only sell 19152 unique wands. – David Z Oct 8 '12 at 23:15
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    I'd remove flexibility from your calculation honestly, because flexibility is probably determined by a combination of length and type of wood (harder wood vs softer wood) – Stephan Jan 14 '15 at 0:23
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    Are any of the three cores incompatible with a particular wood in any way? – DCOPTimDowd Feb 17 '17 at 21:00

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