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# 5-digit Number

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5-digit Number - Back to the Number Puzzles

What 5-digit number has the following property? If we put numeral 1 in front of the number, we get a number three times smaller, than if we put the numeral 1 behind this number.

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5-Digit Number - solution

Using an easy equation: 3(x+100000) = 10x+1 we find out that the number is 42857.

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10007

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Posted · Report post

42857

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There is actually another way to solve this puzzle, figuiring out the answer digit by digit, backwards.

Can someone figure out what it is?

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There is actually another way to solve this puzzle, figuiring out the answer digit by digit, backwards.

Can someone figure out what it is?

Yes, I did it this way. It is slower, but perhaps more fun.

First you write the equation like a long multiplication question:

1 a b c d e

x_______3

a b c d e 1

This is the logic:

e x 3 ends in 1. e must be 7 (7x3=21, carry the 2)

d x 3 ends in 7-2. d must be 5 (5x3=15, carry the 1)

c x 3 ends in 5-1. c must be 8 (8x3=24, carry the 2)

b x 3 ends in 8-2. b must be 2 (2x3=6, no carry)

a x 3 ends in 2. a must be 4 (4x3=12, carry the 1)

1 x 3 ends in 4-1. this is true.

______2

1 a b c d 7

x_______3

a b c d 7 1

_____1

1 a b c 5 7

x_______3

a b c 5 7 1

___2

1 a b 8 5 7

x_______3

a b 8 5 7 1

1 a 2 8 5 7

x_______3

a 2 8 5 7 1

1

1 4 2 8 5 7

x_______3

4 2 8 5 7 1

(carries in yellow)

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Great job!

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I solved algebraically but I had to see zAlbee's way for myself...and it works! Very clever solution

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The original solution doesn't work. It gives you a decimal that, when rounded, gives you the correct answer. But, if you change it to -1 it removes the decimal. Just pointing out that it needs a slight adjustment. It took me awhile and I resorted to guess and check but, thanks to my dad's idea, I used microsoft excel.

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The original solution doesn't work. It gives you a decimal that, when rounded, gives you the correct answer.

No, try it again. The original solution works fine. 100,000 + x = (10x + 1) / 3 resolves uniquely to x = 42,857.

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Very cleaver guys. I tried to not use a calculator, so I made it a little harder for me. I assumed the answer was "55555" to start and did the math and it was close but not right.

Then I tried "33333" and that was close and not right, but it showed me the answer was between the two.

Then I tried "44444" and that was closer and then I knew the answer was between 44444 and 33333.

I got into the right ballpark, but I cheated and looked at this point. At least I narrowed to 11111 possible answers.

which, 11111, is consequently the only 5 digit number thats solution is exactly the same when you ad a 1 to the beginning or end. LAUGH!!!

Edited by IceCreamTruck
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As you call it"the original solution"does work,doesn't give you any decimal just because is the correct equation.If you can't construct such a simple one by your own,at least try to do the math by puting the given number at "x" place and you'll find out,that everything is o'k.Personaly.for me is more fun to solve it digit by digit,because is to fast with the equation.

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.11111 the furture you go away from the point the smaller it ggets

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I found almost but because of my lack of understanding on question.. I thought 5 digit number including '1'.

so I ended up till

28571

and 12857

If I would have tried for next number.. ie 6th I had found the answer.. Anyway misunderstanding is also a type of FAIL

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the five digit number is 42857, it satisfies the given condition.

1st condition: five digit number [i.e., 42857]

2nd condition: if the digit 1 is placed before the five digit number [i.e., 42857] the number is now 142857 which should be three times the number which is formed when the digit 1 is placed after the five digit number [i.e., 428571], which obviously is true.

In mathematical solution,

142857= 1/3(428571)

=142857

Very cleaver guys. I tried to not use a calculator, so I made it a little harder for me. I assumed the answer was "55555" to start and did the math and it was close but not right.

Then I tried "33333" and that was close and not right, but it showed me the answer was between the two.

Then I tried "44444" and that was closer and then I knew the answer was between 44444 and 33333.

I got into the right ballpark, but I cheated and looked at this point. At least I narrowed to 11111 possible answers.

which, 11111, is consequently the only 5 digit number thats solution is exactly the same when you ad a 1 to the beginning or end. LAUGH!!!

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