St Albans Question

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pinkpanther
Posts: 24
Joined: Wed Sep 12, 2012 8:02 pm

St Albans Question

Post by pinkpanther »

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
WP
Posts: 1331
Joined: Thu Jan 03, 2008 9:26 am
Location: Watford, Herts

Re: St Albans Question

Post by WP »

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.
pinkpanther
Posts: 24
Joined: Wed Sep 12, 2012 8:02 pm

Re: St Albans Question

Post by pinkpanther »

Thank You WP for your help
pinkpanther
Posts: 24
Joined: Wed Sep 12, 2012 8:02 pm

Re: St Albans Question

Post by pinkpanther »

works every time - tried it with 7, 8 and 9 digit numbers as well. Thanks again WP
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