which elemental clues contain sufficient info to place the element using no other info

The atomic number is enough clue that can be used to proper place elements without any other information. The atomic number is the number of protons in an atom. Protons are positively charged particles in the nucleus of an atom.

To place elements on the periodic table, the periodic law which states that "properties of elements are a periodic function of their atomic number" must be obeyed.
Using the atomic number, one can determine the number of electrons in a neutral atom, the charges on an ion e.t.c.
Atomic number can also be used to write the electronic configuration of an atom be it the shell notation, sublevel notation and the lewis dot structure.

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