# Math

I am a number between 1000000 and 2000000. My ones digit is the sum of my tens and hundreds digits and is also the sum of my millions and ten thousands digits.my hundred thousands, thousands, and ones digits are the same.the sum of my digits is 45.what number am i?

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1. I am a number between 1000000 and 2000000
---> 1 ??? ???
my hundred thousands, thousands, and ones digits are the same
---> 1 x?x ??x

---> 1 xax bcx

My ones digit is the sum of my tens and hundreds digits
---> x = b+c

also the sum of my millions and ten thousands digits
---> x = 1 + a

so we know
a+1= b+c
a = b+c - 1

the sum of my digits is 45
1 + 3x + a + b + c = 45
1 + 3(1+a) + a + b + c = 45
1+3+3a+a+b+c = 45
4a + b + c = 41
4(b+c-1) + b + c = 41
4b + 4c - 4 + b + c = 41
5b + 5c = 45
b+c = 9
c = 9-b

so we have :
c = 9-b
a = b+c-1
x= a+1

let b = 0, c = 9 ,a = 8 , x = 9 --> 1,989,099
let b = 1, c = 8, a = 8, x = 9 ---> 1,989,189
let b = 2, c = 7, a = 8, x = 9 ---> 1,989,279
...
let b = 8, c = 1, a = 8 , x = 9 ---> ..........
let b = 0 , c = 9, a = 10 not possible

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posted by Reiny

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