Enigma 1742: Chip-chop
26 March 2013
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From New Scientist #2910, 30th March 2013 [link]
I have a seven-figure number that uses seven consecutive digits in some order. Starting at the left and deleting a digit leaves a six-digit number, then deleting the right-end digit leaves a five-digit number, then deleting the left-hand end digit leaves a four-digit number, and so on, alternating sides until a single digit is left. Looking at the list of seven numbers obtained in this way I see that they are all odd, and that only the six-digit number is divisible by 3 (but not 9). Surprisingly, if I had carried out the process starting by deleting the right-hand end digit and then the left, and so on down to a single digit, all the above facts would still be true.
What number did I start with?