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# ​​𝕡𝕃𝕖𝔸𝕤𝔼 𝕙𝔼𝕃𝕡!!!

+1
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One day, River writes down the numbers 1,2,3,...999

What is the sum of all the digits that River wrote down?

May 3, 2020

#1
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Using the formula $$\frac{1}{2}(n)(n+1)$$, we substitute the $$n$$ as $$999$$ to get $$\boxed{499500}$$.

May 3, 2020
#3
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sorry, but it says it's wrong... thanks for helping though :)

edited by lokiisnotdead  May 3, 2020
#2
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This is an arithemtic series with d = 1

S = (n/2) × (2a + (n−1)d)

S = sum = 999/2 (2 + 998(1))

= 499500

May 3, 2020
#5
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sorry, that's wrong too... thanks for taking the time to help though :)

#4
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Just to clarify: the problem asks the sum of all the digits that he wrote down.

May 3, 2020
#6
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189 , 300 , 300 , 300 , 300 , 300 , 300 , 300 , 300 , 300 >>Total = 2889

May 3, 2020
#8
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thanks Guest! even though this isn't the answer, your explanation was the part I was stuck on! (I couldn't figure out how many 1s, 2s, 3s, etc. there were)

So the answer is 1+2+3...9 =45 *300 = 13500.

#9
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Sorry, I did have both of them but didn't read the question correctly:

(189, 300, 300, 300, 300, 300, 300, 300, 300, 300) >>>Total Number = 2889
(0, 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700)>>Total Sum = 13500

Guest May 3, 2020
#10
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great job Guest!

thanks for helping!!! I really appreciate it :)))

#7
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Each digit is written 99 times, so the sum is (0 + 1 + 2 + ... + 9)*99 = 4455.

May 3, 2020
#11
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This is an AoPs question from counting and probability...

STOP POSTING AOPS QUESTIONS HERE

May 4, 2020