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 Post subject: St Albans QuestionPosted: Sun Dec 30, 2012 12:22 pm

Joined: Wed Sep 12, 2012 7:02 pm
Posts: 24
I can't copy the image so I'm going to type out the question.

I have the correct answers but I don't understand the logic behind it.

The number "one two one zero" i.e. the number 1210, has a peculiar property,

0 1 2 3 (Digits)
1 2 1 0 (Number)

The first digit is the same as the number of 0's in the number. The second digit i8s the same as the number of 1's in the number, and so on. i.e. the number 1210 has 1 zero, 2 ones, 1 two, and 0 threes.

a) find another 4 digit number with the same property

0 1 2 3 Digits
2 0 2 0 Number (answer is correct)

b) find a five digit number with the same property

0 1 2 3 4 Digits
2 1 2 0 0 Number (answer is correct)

c) find a ten digit number with the same property

0 1 2 3 4 5 6 7 8 9 Digits
6 2 1 0 0 0 1 0 0 0 Number(answer correct)

My son and DH worked out the answers through sheer graft using 'hit and miss theory' and determination, but we need the logic behind it to see how to work out the answer properly.

Any help would be appreciated. Thanks

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 Post subject: Re: St Albans QuestionPosted: Sun Dec 30, 2012 5:13 pm

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1322
Location: Watford, Herts
A 4-digit number with this property must have digits summing to 4, that is:
• two 0s, a 1 and a 3 (2101), or
• two 0s and two 2s (2020), or
• a 0, two 1s and a 2 (1210).
The first one doesn't work, but the other two do.

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 Post subject: Re: St Albans QuestionPosted: Tue Jan 01, 2013 11:28 am

Joined: Wed Sep 12, 2012 7:02 pm
Posts: 24
Thank You WP for your help

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 Post subject: Re: St Albans QuestionPosted: Wed Jan 02, 2013 9:38 pm

Joined: Wed Sep 12, 2012 7:02 pm
Posts: 24
works every time - tried it with 7, 8 and 9 digit numbers as well. Thanks again WP

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