11 November 2019
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From New Scientist #1677, 12th August 1989 [link]
There is something unusual about my home and office telephone numbers, which both contain six digits.
For example, both are made up of only odd digits, and both are palindromes, that is, they read the same backwards or forwards. Also, no individual digit occurs more than twice in either of the numbers.
However, the most unusual thing about the numbers is that all the digits in them are factors of the number itself. In other words, if I choose any digit in my home telephone number, it will divide exactly into my home number, and likewise with my office number.
If my home number is larger than my office number:
(a) What is my home telephone number?
(b) What is my office telephone number?
Enigma 1452 is also called “Crossed lines”.
22 July 2019
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From New Scientist #1661, 22nd April 1989 [link]
I have two accounts at Midloids bank, both with unusual eight-digit account numbers, which are made up of a combination of only odd digits.
If either of the account numbers is split in half it gives two four-digit prime numbers. These two primes contain the same four digits, but in a different order, and with no digit repeated. Furthermore if these four-digit primes are split in half, they each give two two-digit prime numbers.
If, for both numbers, the prime formed from the first four digits is larger than the prime formed from the second four digits, what are the numbers of my accounts?