Maths - Number Conversions

See if you can convert these numbers into base 10 given the base they are currently written in.
For example, if the base was 4 and the number was 232, then the answer would be 2*16 + 3*4 + 2*1 = 46.
Some working out paper would be extremely helpful for some questions.
Quiz by mushroomsteve
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Last updated: July 30, 2016
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First submittedMarch 22, 2016
Times taken73
Average score45.0%
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Base
Number
Number in Base 10
2
1010
10
2
10011
19
2
11101
29
2
101000
40
2
1101001
105
2
10111101
189
3
212
23
3
11211
130
4
123
27
4
3333
255
Base
Number
Number in Base 10
5
421
111
6
1352
356
7
6666
2400
8
7022
3602
9
1248
935
11
29A
351
12
B15
1601
16
ACE
2766
16
8D1
2257
16
F1F1
61937
+1
Level 76
Mar 22, 2016
nice!
+1
Level 53
Mar 23, 2016
Thanks!
+1
Level 53
Jul 30, 2016
Please tell me if you are able to work out the last one in your head (without using paper).
+1
Level 60
Oct 29, 2016
this is how I did it:

F1F1 = F01 x 101 (both in base 16) = 241 x 257

Then I used a bunch of mental calculation tricks:

241 x 257 = 249^2 - 8^2

249^2 = 248x250 + 1 = 62x1000 + 1 = 62001

so F1F1 = 62001 - 64 = 61937

Took me about 2 minutes because I subtracted one instead of adding one the first try :P

Thanks for the puzzle, haha

+1
Level 60
Oct 29, 2016
on hindsight, it may have just been easier to take 15*4096 + 256 + 15*16 + 1
+1
Level 53
Oct 30, 2016
That is clever! Before, I did F1F1 = 241 x 257 in my head, but I couldn't do 3 digit by 3 digit multiplication in my head without a high risk of mistakes. I really should have thought of the 8^2 thing. Thanks for sharing your solution!
+1
Level 74
Oct 6, 2017
yeah, kind of did the same as 81929128's last thought: F*(1010) + 101->15*(4096+16) + 257 ... though confess to having to write down a couple of intermediate stages in the answer box as I was going!
+1
Level 38
Feb 20, 2021
Finished with 7:23 remaining (in 12:37)