Fiona's Telephone Number

Pro Problems > Math > Number and Quantity > Number Theory > Digits

Fiona's Telephone Number

When Shrek asks Fiona for her telephone number, Fiona is a bit coy about it, and tells Shrek the following information:

My telephone number has 10 digits.
There are no repeated digits in my telephone number.
The first three digits are in ascending order.
The second three digits are in descending order.
Both the last four digits and the last two digits are multiples of sixty.
My last four digits are not a multiple of 43.
My first three digits are the square of an integer less than twenty.
The sum of the second three digits is 14.

What number should Shrek dial?

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Problem by madelynK

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