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Using digits 1,2,3,4,5,6,7,8,9 only once how do you equal 1 million.

Adding, multiplication, subtraction and division

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    Using the numbers 1,2,3,4,5,6,7,8,9 only once how can you construct the number 1 million using only addition, multiplication, subtraction and division. Intermediate numbers can be created using addition and multiplication by 10, but these numbers can not contain factors of 10.2012-10-01

5 Answers 5

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Assuming you can construct number from digits one way to do it the following $625*4*8(19*3-7)=5^42^22^3(57-7)=5^42^5*50=5^4*2^5*5^2*2=10^6$

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    @robjohn Yes, my first one:)2012-10-02
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Without some more options of operations, I don't think you can get there, as $9!=362880$. Powers would make it easy: $(1+9)^{(2*3+4+5+6-7-8)}=(1+2*3+4+5-7-8+9)^6$

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    Still too small, but showing that the 9! argument does not work.2012-10-03
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As Ross Millikan notes, this can't be done using each digit as a complete number, so I assume that building numbers from the digits is allowed.

For example: $(7814\times2-3)\times(69-5)=1000000$

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Also assuming powers: $((-1\times3+6\times9+7-8)\times4\times5)^2$

Actually $1 + 2 + 3 + 4 + 5*6 + 7 + 8 + 9 = 64 = 1000000_2$

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    What are these strange symbols: $2,3,4,5,6,7,8,9$? Oh! they're that base-$1010$ encoding I've heard of.2012-10-01
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$(1+2+3+4)^6 \times (7-5-9+8) = 10^6 \times 1 = 1000000.$