Easy #2

Number Theory Level 3

How many four-digit numbers of the form 6 A 4 B 6A4B ( A A and B B are digits) are divisible by 36 36 ?


The answer is 4.

Victor Loh by Victor Loh , 19, Singapore

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1 solution

Aaaaa Bbbbb
Jul 27, 2014

So having 4B=40|44|48 and 10+A+B=9K ⇒ B = 0 ∣ 4 ∣ 8 , 1 + A + B = 9 ∣ 18 \Rightarrow B=0|4|8, 1+A+B=9|18 ⇒ A = 8 ∣ 4 ∣ 0 , 9 \Rightarrow A=8|4|0,9 The numbers satisfies the condition are: 6840, 6444, 6048, 6948 R e s u l t = 4 Result = \boxed{4}

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