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9-digit Number

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9-digit Number - Back to the Number Puzzles

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

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9-Digit Number - solution

473816952 – if rounding changes the next numeral character

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Posted · Report post

I dont think my head can go that far. im Guessing the number 123456789

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Posted · Report post

your solution does not make sense based on the criteria you gave. Could you explain how you came up with your solution please.

in your number, you did not alternate rounding up and down and you rounded the last number which in your directions you said not to do and after your fourth time rounding, the remaining numbers add up to 23 not 24.

I hope you can explain your solution, because I am very confused at this point as i had a very different solution.

thank you

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Posted · Report post

the numbers work 473816952 you still round up for the first one, down for the second one, up for the third one and so on, then the numbers add up to 24 and it works

2 rounds down to zero, 5 stays the same

5 rounds up to zero, 9 adds one becomes 0

0 rounds down zero, 6 stays a six

6 rounds up to zero, 1 adds one becomes 2

2+8+3+7+4 =24

finish rounding numbers and you end up with

500000000

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Posted · Report post

I came up with another answer. The problem says "The rounding alternates (up, down, up ...)" so I started rounding up, not down first. Here is what I came up with, I believe it meets all the criteria of the problem:

518372946

Adam

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Posted · Report post

Is there any other way to do this besides trial and error?

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Posted · Report post

[

I came up with another answer. The problem says "The rounding alternates (up, down, up ...)" so I started rounding up, not down first. Here is what I came up with, I believe it meets all the criteria of the problem:

518372946

Adam

Adam, yours does not alternate.

follow:

5183729846 -- round up

5183729850 -- round up again!

5183729900 -- and we round up again...and so forth.

I think you probably just missed that 4 going up to a 5 since it would alternate other than that!

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Posted · Report post

Adam:

I came up with another answer. The problem says "The rounding alternates (up, down, up ...)" so I started rounding up, not down first. Here is what I came up with, I believe it meets all the criteria of the problem:

518372946

Perhaps Adam begins on the incorrect end. Instructions indicate one is to begin with the units, then 10's and so-on. Otherwise, he would be correct.

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Posted · Report post

your solution does not make sense based on the criteria you gave. Could you explain how you came up with your solution please.

in your number, you did not alternate rounding up and down and you rounded the last number which in your directions you said not to do and after your fourth time rounding, the remaining numbers add up to 23 not 24.

I hope you can explain your solution, because I am very confused at this point as i had a very different solution.

thank you

You make one mistake here: after the forth rounding (up), the 1 would have become a 2, and the sum of the remaining numbers would then INDEED be 24!

This was an easy onion to peel.

BoilingOil

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Posted · Report post

Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn):546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

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Posted · Report post

Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn):546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

as already mentioned above by savagegamer90 and Boiling Oil ... the sum of the remaining numerals after 4 round-offs is indeed 24

after 1st rounding - 473816950

after 2nd rounding - 473817000

after 3rd rounding - 473817000

after 4th rounding - 473820000

so 4+7+3+8+2=24

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Posted · Report post

Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn):546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

your answer isn't right because your number isn't commensurable by 6 or 7 ( i had to look it up, from what I read commensurable basically means divisible by) so the number was supposed to be divisible by 6 and 7, which the original answer is

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Posted · Report post

Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn):546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

u r incorrect.

550000000 rounds to 600000000

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Posted · Report post

Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn):546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

u r incorrect.

550000000 rounds to 600000000

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Posted · Report post

My solution:

542673198

Chk it!

divisible by 6 & 8..

round off till end n u will get 500000000

also last 5 digits will add to 24 in the process...

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Posted · Report post

My solution:

542673198

Chk it!

divisible by 6 & 8..

round off till end n u will get 500000000

also last 5 digits will add to 24 in the process...

542673198 is not divisible by 7 (as the puzzle requested)

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Posted (edited) · Report post

This is unsolveable. Round to what? The nearest multiple of 10? The nearest multiple of 5? The nearest multiple of 2?

Edited by sunshipballoons
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Posted · Report post

This is unsolveable. Round to what? The nearest multiple of 10? The nearest multiple of 5? The nearest multiple of 2?

round to insanity :lol:

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Posted · Report post

Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn): 546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

The initial answer did look correct to me (I think the description of alternate rounding, wasn't meant to say it HAS to round up first, rather it was a specifc example presented to illustrate what was meant by alternate rounding).

There are a few issues with the alternative solution you presented:

Your sum after 4 rounds of rounding equals 25

Also, your final round down, should have been a round up (given that the 5 dictates a round-up)

Last but not least, your intial number is not divisible by 7 nor 6

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