The need for the development of new superconducting materials is increasing from an academic or applied point of view. We have succeeded in discovering many new superconductors [1-5] using the “bulk-combinatorial method”. This time we will elaborate on this method in detail. We also show that the problem that arises when identifying new superconductors in this method is related to the combinatorial mathematics, and is also related to the famous mathematical puzzle so called “1000 poisoned wine bottles” under certain assumptions.

[1] A. Iyo et al. Sci. Rep. 5 (2015) 10089.
[2] A. Iyo et al. Inorg. Chem. 56 (2017) 8590.
[3] A. Iyo et al. Phys. Rev. Mater. 3 (2019) 124802.
[4] A. Iyo et al. Inorg. Chem. 59 (2020) 12397.
[5] A. Iyo et al. in preparation.

Fig.  Left panel: “mild mixture” of ingredients using for bulk-combinatorial method. Utilizing inhomogeneity of the sample, we can synthesize various compounds at once. See dotted circle and dashed circle.  Right panel: We can even prepare multiple sets of pellets and synthesize them in a high-pressure cell simultaneously.

Keywords: superconductivity, bulk-combinatorial method, combinatorial mathematics, mathematical puzzle