Life is A Test 2: Test Harder (Quite A Bit Harder)

by Brony_of_Brody

The Answer 40

Following logic, one can estimate the answer to be 18.4 quintillion.

The tenth term, or 2¹⁰, is 1024. That's roughly 1000, a nice round number. So if 1000 is roughly 2¹⁰, then a thousand times itself six times is equal to 2¹⁰ multiplied by itself six times, to make 2⁶⁰.

1000⁶ is one quintillion. So 2⁶⁰ is approximately equal to a quintillion.

The remaining 2⁴ equals sixteen, so 2⁶⁴ is 2⁶⁰ x 2⁴, equalling 16 quintillion.

That's not bad, but we can definitely use a bit more logic to make this more precise.

We approximated 2¹⁰ as 1000. But 1024 is 2.4 percent bigger than 1000. So every time we multiplied by a thousand, we should have also added on the remaining 2.4%. Multiplying a thousand by itself six times means we should have added on six lots of 2.4%, to make about 15% total. So the answer is 16 quintillion plus an extra 15%.

Luckily, it isn't difficult to work out 15% of 16 quintillion. Ten percent of it is 1.6 quintillion, so five percent of that is 0.8 quintillion, to make a total of 2.4 quintillion, which we add on to make 18.4 quintillion.

BTW, the exact total is 18,446,744,073,709,551,616.