Magical Square Numbers #2

Number Theory Level 1

If 2^(10a+b) is a 9 digit number such that it contains all the numbers except 4. Find a+b.

5 11 7 9

Saurav Pal by Saurav Pal , 26, India

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3 solutions

Saurav Pal
Apr 5, 2014

If 2^X is a 9 digit number. Then 26<X<30. So, X=29.

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Sujay Sheth
May 7, 2014

Trial and error 2^29 = 536870912

(10a+b) = 29

Thus, a =1 and b = 19 or a = 2 and b = 9

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Emmanuel David
Apr 29, 2014

2^(10a+b) = 9 digit number

(10a+b) is equal or greater than 27 but equal or less than 29

then (10a+b) = 29 through trial and error because 2^29 = 536870912

then a couldn't be greater than 20 making a = 2

10(2)+b = 29

20+b = 29

20+b-20 = 29-20 SPE

b = 9 Subtraction Fact

a = 2 and b = 9

2+9 = 11 :D

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