She's the 1.66053886(28) × 10-24 moles

Here's a useful google calculator calculation: How many moles is a baker's dozen?. The google calculator will return any dimensionless unit in moles if you ask nicely, such as lightyear/foot (both distances), or kilogram/electron mass (both masses). The former means that a mole of footsteps will transport you millions of lightyears, the latter that a mole of electrons will weigh much less than a bag of sugar.

Google calculator thinks that a mole is just a large number. This is how I would think of it, too. The official definition of a mole is, however, as follows.

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

An amount of substance is "defined to be proportional to the number of specified elementary entities in a sample".

This is of course a load of bollocks (number yet unspecified, but hopefully less than a mole). The phrase "atoms, molecules, ions, electrons, other particles" is ridiculous. Do other particles include cows, donuts, shoes, ships and tins of sealing wax? If not, why not? If so, why not add a couple to the list:

...the elementary entities must be specified and may be atoms, molecules, cows, ions, dildos or other particles.

And don't go all "complex objects" and "elementary particles": an atom isn't elementary in the slightest, and despite the name can be cut open at will.

Why do the SI want to make this distinction between "elementary entities" and everyday objects? Why not use moles to count things? The problem is that the mole is defined in terms of kilograms, and the definition of a kilogram is "equal to the mass of the international prototype of the kilogram." The fact that all known masses are dependent on a lump of metal in Paris staying intact has annoyed scientists for a while. One cow is presently 1.66053886 x 10-24 moles of cows, but if the prototype kilogram loses mass—and in the last century it did—it could in the future be less.

Another problem is that nobody knows quite how many units are in a mole. This is why there is a (28) in the brackets of the title. This means that you could add (or subtract) 28 to (or from) the last two digits (86) and still be within the margin of error. So a cow could as much as 1.66053904 x 10-24 moles of cows, or as little as 1.6605358 x 10-24 moles of cows.

So presuming google calculator and I are correct in treating the mole as a counting unit (and who would wish to doubt this), all scientists don't know how many things they have, and are continously losing/gaining them too, depending on a lump of metal in Paris.

One way out of this crisis would be to count in units (the one), and define the kilogram in terms of electron masses. Thus scientists could again count with with the rest of the population. I don't think the chemists would like it, though.

As a reward for sticking with this post, here is The Answer in moles.

[Disclaimer: The Answer in moles contains error bars and may increase or decrease with time. The author accepts no responsibility for future changes to The answer in moles.]