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Group testing (GT) is the Boolean counterpart of compressed sensing and themarketplace of new ideas for related problems such as cognitive radio and heavyhitter. A GT scheme is considered good if it is nonadaptive, uses $O(k \log n)$tests, resists noise, can be decoded in $O(k \operatorname{poly}(\log n))$time, and makes nearly no mistakes. In this paper, we propose "Gacha GT", anelementary, self-contained, and unified randomized scheme that, for the firsttime, satisfies all criteria for a fairly large region of parameters, namelywhen $\log k < \log(n)^{1-1/O(1)}$. Outside this parameter region, Gacha can bespecialized to outperform the state-of-the-art partial-recovery GTs,exact-recovery GTs, and worst-case GTs.  The new idea that runs through this paper, using an analogy, is to ask everyperson to break her $9$-digit "phone number" into three $3$-digit numbers $x$,$y$, and $z$ and write $(b, x)$, $(b, y)$, and $(b, z)$ on three pieces ofsticky notes, where $b$ is her "birthday". This way, one can sort the stickynotes by birthday to reassemble the phone numbers. This birthday--number codeand other coded constructions can be stacked like a multipartite graph pyramid.Gacha's encoder will synthesize the test results from the bottom up; andGacha's decoder will reassemble the phone numbers from the top down.

Noise-Resilient Group Testing with Order-Optimal Tests and Fast-and-Reliable Decoding