Thank you all ever so much.

It is very interesting to know what is the cause of this situation...

It seems very strange such a big time difference for the function LengthWhile.

It is the worst choice!

In[1]:= tList = RandomChoice[{"a", "b", "c"}, 1000000];
tList[[777777]] = 1;

In[3]:= Position[NumericQ /@ tList, True][[1]] // AbsoluteTiming
Position[tList, _?NumericQ, 1] // AbsoluteTiming
Position[tList, _?(NumericQ[#] &), 1] // AbsoluteTiming
FirstPosition[tList, _?NumericQ, 1] // AbsoluteTiming
FirstCase[tList, _?NumericQ] // AbsoluteTiming
SelectFirst[tList, NumericQ] // AbsoluteTiming
(LengthWhile[tList, Not@*NumericQ] + 1) // AbsoluteTiming

Out[3]= {0.369993, {777777}}

Out[4]= {0.39994, {{777777}}}

Out[5]= {0.820059, {{777777}}}

Out[6]= {0.32599, {777777}}

Out[7]= {0.302233, 1}

Out[8]= {0.211421, 1}

Out[9]= {2.50185, 777777}

In[10]:= BarChart@{
   Position[NumericQ /@ tList, True][[1]] // AbsoluteTiming,
   Position[tList, _?NumericQ, 1] // AbsoluteTiming,
   Position[tList, _?(NumericQ[#] &), 1] // AbsoluteTiming,
   FirstPosition[tList, _?NumericQ, 1] // AbsoluteTiming,
   FirstCase[tList, _?NumericQ] // AbsoluteTiming,
   SelectFirst[tList, NumericQ] // AbsoluteTiming,
   (LengthWhile[tList, Not@*NumericQ] + 1) // AbsoluteTiming
   }[[All, 1]]

Perhaps start simply and avoid the use of shortcut notation when you aren't sure how things work

In[1]:= Map[NumericQ, {0, -1 + x^2 y^2, -x^3 + 2 x^2 y + x^5 y^2}]

Out[1]= {True, False, False}

and thus you would probably want to get the position of the first False.

There is a new function FirstPosition mentioned at the bottom of the help page on Position

In[2]:= FirstPosition[Map[NumericQ, {0, -1 + x^2 y^2, -x^3 + 2 x^2 y + x^5 y^2}], False]

Out[2]= {2}

Now can we perhaps understand why your _?NumericQ[#] & didn't work? The & turned all that into a function and Position is looking for a pattern as the third argument, not a function.

We can use a pattern with a condition that only matches numeric items, this way

In[3]:= Position[{0, -1 + x^2 y^2, -x^3 + 2 x^2 y + x^5 y^2}, z_ /; NumericQ[z]]

Out[3]= {{1}, {2, 1}, {2, 2, 1, 2}, {2, 2, 2, 2}, {3, 1, 1}, {3, 1, 2, 2}, {3, 2, 1}, {3, 2, 2, 2}, {3, 3, 1, 2}, {3, 3, 2, 2}}

which does successfully find the position of numeric items, but matches those at every level and that doesn't look like what you were looking for. You could augment that with a level argument like this

In[3]:= Position[{0, -1 + x^2 y^2, -x^3 + 2 x^2 y + x^5 y^2}, z_ /; NumericQ[z], 1]

Out[3]= {{1}}

which shows that only the first item in the list is numeric.

Perhaps you can use some of these ideas to explore further

I just found out there is also SelectFirst, if you don't want the index but rather the element itself...

Dear Bill

Thank you ever so much. I will definitely explore your examples further

Regards

Ed

In[1]:= Position[NumericQ /@ {0, -1 + x^2 y^2, -x^3 + 2 x^2 y + x^5 y^2}, True][[1]]

Out[1]= {1}