For various uses, like simulation of section edit links or to have a count or something similar in section links it would be nice to have an {{NUMBEROFSECTIONS:Pagename}} magic word.
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I think it should be as it is internal, that mean every section is counted no matter which level it has.
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This can't be done, since the number of sections in a page isn't known until after parser functions get evaluated. Imagine a page that contained {{#ifeq:{{NUMBEROFSECTIONS:{{FULLPAGENAME}}}}|0|== Section ==}}. This would cause a paradox.