Given that:
1 1
------------- - -----
√(22-10-2022) √(22)
= 0.00....00ABCD...(N zeros).
Accordingly, exactly N zeros immediately follow after the decimal point, and:
ABCD are base 10 digits, whether same or different, with A being nonzero.
Determine the value of N.
*** As an extra challenge, solve this puzzle without using computer program or excel solver.
digits 12000
a=vpa(1)/sqrt(vpa(22)-vpa(10)^-2022);
b=vpa(1)/sqrt(vpa(22));
disp(a-b)
disp(log(a-b)/log(10))
shows the common log of the difference as being about
-2024.3146640168970997
indicating 2024 zeros after the decimal point and before the first non-zero digit.
Also, a direct count of the zeros (position of the last zero before the non-zero 4 in the display of a-b minus the position of the decimal point) shows it's 2024.
That's the value of N, 2024, the desired answer.
Then, for curiosity's sake:
>> l=log(a-b)/log(10)
l =
-2024.3146640168970997
>> l2=l+2024
l2 =
-0.3146640168970997
>> 10^l2
ans =
0.48454708262660027489
shows ABCD = 4845, also in agreement with the direct display of the value.
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Posted by Charlie
on 2022-03-09 13:08:19 |
solution (spoiler)
