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Jane wants to create a six-digit number for her padlock. She writes down two digits and each digit she writes after these is the sum of the previous two digits. How many six-digit numbers could she create in this way? (A number may not start with the digit zero).

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*