余す: full use of available strength and all the materials
Read 余すところなく and 余すことなく as leaving none unused, with the athlete's available strength and the materials as their stated bounds.
Read the negative combinations together
余す (あます) means to leave unused or spare. In these examples, 余すところなく and 余すことなく describe using strength and materials without leaving any unused.
Read ところなく and ことなく with 余す rather than turning the sentences into statements that strength or materials remained. The bounds are the athlete's available strength and the materials mentioned.
Available strength and complete material use
「選手は持てる力を余すところなく発揮した。」 (The athlete used every bit of available strength.) The athlete actually used all the strength available. 持てる力 sets that available scope; it does not include every outside resource or establish a victory.
「材料を余すことなく使い切った。」 (We used all the materials without leaving any.) The materials were actually used up with none left over. Read 余すことなく together with 使い切った to preserve that complete use rather than a partial remainder.
Full use within the stated resources
余すところなく connects to exerting available strength, and 余すことなく connects to using the materials. Both describe full use within the resource named in their sentence.
Using every bit of strength does not supply a victory or a perfect performance. Using all the materials likewise does not state that a perfect work was produced. Keep resource use separate from those further outcomes.
Do 余すところなく and 余すことなく say that some strength or materials were left unused?
Show the answer and why
In these sentences, they say that the available strength was fully used and the materials were used up. They do not add a victory or a perfect finished work.