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Author Topic: Piotr's number puzzle  (Read 843 times)
tpog
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« on: June 06, 2009, 08:34:24 PM »

Tell me the example of a natural number (0,1,2,3,etc.) that when we take off the first digit we'll get a higher number as a result.

In example for 23, we'll take off the first digit, the result is 3. But unfortunatelly 3 is not higher than 23. So find another number(s) that will be the answer.

 huh
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« Reply #1 on: June 06, 2009, 08:44:01 PM »

I don't understand the cause of making a new thread, you didn't ask a question nor post a relevant subject.
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Warlock
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« Reply #2 on: June 06, 2009, 08:59:40 PM »

Is there any?
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« Reply #3 on: June 06, 2009, 09:00:49 PM »

I don't understand the cause of making a new thread, you didn't ask a question nor post a relevant subject.

There are a lot of things I don't understand, as well.
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« Reply #4 on: June 06, 2009, 09:35:28 PM »

32465 ?
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« Reply #5 on: June 06, 2009, 09:43:31 PM »

2465<32465
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« Reply #6 on: June 06, 2009, 11:33:32 PM »

how about -42
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inp o҉rtb
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« Reply #7 on: June 06, 2009, 11:46:39 PM »

how about -42

-42 is not a natural number.
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« Reply #8 on: June 06, 2009, 11:52:06 PM »

how about -42
Natural numbers = non-negative, non decimal numbers.
Wink

Edit: Awww, inp o҉rtb got there first.
« Last Edit: June 06, 2009, 11:58:35 PM by uh_Iforgot » Logged

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« Reply #9 on: June 07, 2009, 12:07:10 AM »

0.2 OR ? Duh
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« Reply #10 on: June 07, 2009, 12:41:05 AM »

0.2 OR ? Duh
Not natural numbers...
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« Reply #11 on: June 07, 2009, 01:25:19 AM »

Not natural numbers...
Woops, sorry, didn't read properly. Surely this is impossible as a n-1 digit number will always be smaller than a n digit number. There's got to be some trick... Duh
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« Reply #12 on: June 07, 2009, 01:44:37 AM »

hmm what about 102? Take off the 1 and you are left with 02 which is bigger than 1  rolleyes
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« Reply #13 on: June 07, 2009, 01:54:59 AM »

hmm what about 102? Take off the 1 and you are left with 02 which is bigger than 1  rolleyes
Does that really count? cheesy
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inp o҉rtb
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« Reply #14 on: June 07, 2009, 02:15:53 AM »

how about -42
Natural numbers = non-negative, non decimal numbers.

saywhat?... natural numbers could be represented in any base as long as they're non-negative integers; you could have a hexadecimal natural number if you want.
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« Reply #15 on: June 07, 2009, 02:22:45 AM »

I don't understand the cause of making a new thread, you didn't ask a question nor post a relevant subject.

So what? Nobody is forcing you to visit it.
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« Reply #16 on: June 07, 2009, 02:48:29 AM »

Hehe, thank you, tpog. cheesy
So - anybody? Smiley
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« Reply #17 on: June 07, 2009, 03:11:56 AM »

how about -42
Natural numbers = non-negative, non decimal numbers.

saywhat?... natural numbers could be represented in any base as long as they're non-negative integers; you could have a hexadecimal natural number if you want.
So 0.1 is a natural number?
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« Reply #18 on: June 07, 2009, 03:29:51 AM »

how about -42
Natural numbers = non-negative, non decimal numbers.
saywhat?... natural numbers could be represented in any base as long as they're non-negative integers; you could have a hexadecimal natural number if you want.
So 0.1 is a natural number?

You tell me: is 0.1 a non-negative integer?
Well let's see... any natural number could be expressed as N = Σn(bi·xi), where b is the [positive integer] base, xi is a positive integer, i varies from 0 to n, and n is 1 less than the number of digits in the particular base. For example,
123 = 100·3+101·2+102·1

Suppose we have another natural number M = Σn-1(bi·xi) and n > 0 (that is, Piotr GRD's problem setup). Firstly, we notice that
N-M = bi·xn

Recall that xn is the most significant digit of N, which M lacks. If M > N, then
N-M < 0
bi·xn < 0

If b, i, and xn are non-negative according to the preconditions, we've hit a stumbling block wink
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« Reply #19 on: June 07, 2009, 03:32:58 AM »

o.O

You lost me with Σn(bi·xi)
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