Aggregated encryption
This is at least feasible if you allow a one-time setup where related keys are distributed among the $n$ devices and the master device. There is a primitive known as aggregated encryption which has the following properties:


The $n$ devices $(D_0, \cdots, D_{n-1})$ each receive a secret key $(s_0, \cdots, s_{n-1})$.
The master device receives an "aggregated secret key"; concretely, this will in general be $s = \sum_i s_i$.
Each device $D_i$ can encrypt some message $m_i$ with the key $s_i$.
Given $n$ encrypted messages $(E_0,\cdots, E_{n-1}) = (E_{s_0}(m_0), \cdots, E_{s_{n-1}}(m_{n-1}))$ and the aggregated secret key $s$, the master device can decrypt $\sum_i s_i$, and cannot learn anything more.


This is relatively easy to build using cryptosystem with appropriate homomorphic properties. The article I link to builds it from the ElGamal cryptosystem, however there also exists constructions from the Paillier cryptosystem, which will be more suited to your problem.

Now, given such a primitive, there is a natural way to ensure that the master device can learn all messages, but without knowing from which device they come: in the one-time setup phase, also give to each device $D_i$ his secret index $j = \pi^{-1}(i)$ ($\pi$ is a uniformly random permutation of $\{0, \cdots, n-1\}$, $\pi^{-1}$ is the reverse permutation, $\pi^{-1}(i)$ will be the "pseudonymous index" of the device $D_i$). Let $\ell$ be a bound on the size (in bit) of each message $m_i$ (I assume $\ell$ to be publicly known) Then, to send $n$ message while concealing the identity of the device each message came from, each device $D_i$ with message $m_i$ computes and sends:

$E_i = E_{s_i}(2^{\ell\cdot\pi^{-1}(i)}\cdot m_i)$

Given $(E_0, \cdots, E_{n-1})$ and his aggregated key $s$, the master device can only recover

$M = \sum_{i=0}^{n-1} 2^{\ell\cdot\pi^{-1}(i)}\cdot m_i = \sum_{j=0}^{n-1} 2^{\ell \cdot j}\cdot m_{\pi(j)}$

Which is exactly the value $m_{\pi(0)} || m_{\pi(1)} || \cdots || m_{\pi(n-1)}$ (when padding each message $m_i$ with zeroes such that it is exactly $\ell$ bit long), id est, all the messages of the devices in some fixed secret permuted order.

Note that an ElGamal-based scheme would not work here since you need your aggregated scheme to support a very large message space, but the Joye-Libert scheme has no restriction on the message space, and should work fine here.