Magic Numbers
Posted: Sun Jul 25, 2010 5:11 pm
Having just watched this reincarnation of Talking Telephone Numbers for the first time, it got me thinking of a puzzle.
For those who are unfamiliar, Magic Numbers is a (pretty terrible) game show where they generate six (single digit) numbers, and then if two of these feature in the last six digits of your mobile or landline phone number then you can call up to enter the draw to play the prize game at the end of the programme. For instance, if your phone number ended 123456 and the show's six numbers were 5,6, 7, 8, 9 and 0 you would win (you've 'matched' 5 and 6), but if your phone number was 123455 you wouldn't (you've only 'matched' 5)
Ignoring dialling codes, there are one million different possible phone numbers (000000 to 999999). If the six numbers they generate on the show are all different, how many of these million phone numbers will match at least two of the show numbers and be 'winners'?
(For clarity, on the show they say that "if two or more of these numbers are in the last six digits of your phone number", which I am taking to mean that repeated numbers are irrelevant. Therefore it is impossible to win if all six digits of your phone number are the same.)
For those who are unfamiliar, Magic Numbers is a (pretty terrible) game show where they generate six (single digit) numbers, and then if two of these feature in the last six digits of your mobile or landline phone number then you can call up to enter the draw to play the prize game at the end of the programme. For instance, if your phone number ended 123456 and the show's six numbers were 5,6, 7, 8, 9 and 0 you would win (you've 'matched' 5 and 6), but if your phone number was 123455 you wouldn't (you've only 'matched' 5)
Ignoring dialling codes, there are one million different possible phone numbers (000000 to 999999). If the six numbers they generate on the show are all different, how many of these million phone numbers will match at least two of the show numbers and be 'winners'?
(For clarity, on the show they say that "if two or more of these numbers are in the last six digits of your phone number", which I am taking to mean that repeated numbers are irrelevant. Therefore it is impossible to win if all six digits of your phone number are the same.)