Eat the gamma cookie, it's the worst option for any, but with gamma it won't matter much whether it's in your hand, pocket or gut.

Pocket the beta emitter, a little bit of shielding will make a big difference.

Hold the alpha emitter, if you hold it with just a pair of fingers you will be able to reduce you dosage a lot compared to holding it tightly.

wouldn't alpha be mostly stopped just in pocket ? I'd hold beta emitter, less area of body affected by the radiation if you hold it at distance

IIRC:

* Alpha in hand. Eaten, the "shielding" that blocks it will actually be very active living cells, leading to severe health outcomes. Your external layers of dead skin cells will be be fine, putting it in your pocket would be excessive.

* Gamma in hand, because whether it's in your hand or in your pocket, it's roughly the same risk, and most of it is actually going through you without stopping to have an effect. (Compared to other two.)

* Beta in pocket, where the additional clothing layer(s) offer some meaningful protection compared to your hand.

The "twist" behind the exercise involves how people often assume penetrative power is proportional to danger, when in some ways it's really the opposite. (Consider the danger profile of neutrinos.)

Oh, I thought you have to choose one of the options for each cookie, no repeats

I guess in that case it would be to eat gamma? Assuming you're keeping all three long-term, the gamma particles will be washing over you whether they're inside you or out.

You're quite correct, the light of the morning and flu-medicine what I should've written is:

* Gamma is [eaten], because whether [wherever it is], it's roughly the same risk, and most of it is actually going through you without stopping to have an effect. (Compared to other two.)

Naturally there's a whole bunch of unstated "all else being equal" going on, where no cookie's' elements are extra-likely to be permanently incorporated into your bones versus excreted, etc.

Same with x-rays. People tend to think “soft” X-rays are safer because they are quickly absorbed by tissue without passing through.

The radiation that passes through is not the problem.

Sure, using the ambiguous wording to assume the cookies all have such a large activity they are unsafe no matter how they are stored is technically a solution. But it's equally possible the teacher is imagining the cookies as only slightly radioactive such that it is indeed possibly to safely store them according to the alternatives given if you choose the correct pairs.

Can these cookies be weaponized? Are there secret cookie enrichment factories? Would weapons-grade cookies still be good with milk?

Only weapons-grade milk.

Heavy milk (whole) is required for cookie enrichment. But depleted milk (skim) still has value.

Commonly used as a projectile