Number base wiki

Number Theory Level 3

Andrew chooses a certain number in base 10 and writes it in base 2. Now this new number (with the base ignored) is the same as 49 written in base 7. Which number did Andrew choose?

Note: 49 is in base 10.


The answer is 4.

Nihar Mahajan by Nihar Mahajan , 20, India

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1 solution

49 = 1 × 7 2 + 0 × 7 1 + 0 × 7 0 ⇒ ( 49 ) 10 = ( 100 ) 7 49 = 1 \times 7^{2} + 0 \times 7^{1} + 0 \times 7^{0} \Rightarrow (49)_{10} = (100)_{7} .

Now, ( 100 ) 2 = 1 × 2 2 + 0 × 2 1 + 0 × 2 0 = ( 4 ) 10 (100)_{2} = 1 \times 2^{2} + 0 \times 2^{1} + 0 \times 2^{0} = \boxed{(4)_{10}} .

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Moderator note:

Simple standard approach.

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