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Staggering Digits (Posted on 2016-07-28) Difficulty: 3 of 5
Find the last three digits of this number:

97532

*** For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
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Solution needed a computer | Comment 2 of 4 |
Using UBASIC as an extra-precision calculator, and when necessary taking mod 1000:

a=3^2:?a
 9
OK
b=5^a:?b
 1953125
OK
c=7^b
Overflow
c=7^125
OK
?c
 4337654948097993282537354757263188251697832994620405101744893017744569432720994
168089672192211758909320807
OK
d=9^807:?d
 1184963893987295289066925399085797252528416947990192243936766628102736110245160
85940878149054929150882379475452715251155610041467428451122186791119754864638395
19520876377020510170039501259690329262206087405943590655866848643350929530736974
93188768572347114745347064492758175486683606686408612355383689429160398632776121
86155578251759604753059443981156526934067543844696670701351202466465394462678493
33279327669235587649148421328570731455180066463340852740184519671258273341204627
32853256807470259039341592060608859697615237982261223794227808949616789154769162
65976259944037197478419889453747194306222323408272026469985446927385047844184321
84082994874946951147913168985987384907486577112634514564468888537995041365635878
2207698046731806249444966661029268852284157809870969
OK

The last three digits are 969.

The number itself, I believe, has 10^1650582.089061605 digits, if I'm doing my logs of logs correctly.

  Posted by Charlie on 2016-07-28 15:12:04
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