# 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 submitted March 22, 2016 Times taken 75 Average score 45.0% Report this quiz Report
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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
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Level 77
Mar 22, 2016
nice!
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Level 53
Mar 23, 2016
Thanks!
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Level 53
Jul 30, 2016
Please tell me if you are able to work out the last one in your head (without using paper).
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Level 61
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

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Level 61
Oct 29, 2016
on hindsight, it may have just been easier to take 15*4096 + 256 + 15*16 + 1
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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!
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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!
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Level 38
Feb 20, 2021
Finished with 7:23 remaining (in 12:37)