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| Math Central | Quandaries & Queries |
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Question from David: Hello. I have the digits "1159" and need to come up with a complete list of possible four-digit combinations. It does NOT matter the order of the two number ones (1), so this will help eliminate many possibilities. Separately, it would also help to actually know the actual number of combinations with which I am dealing to start. Please help when you can. Thank you! David :) |
Hi David,
Look at the response I just sent to Theresa about four digit numbers made from 1-2-3-4. Repeat my solution using the digits 1-2-5-9. How many did you get?
Every 4 digit number in your list has an "almost twin", one where the 1 and 2 are reversed, for example 1572 and 2571. Now replace each 2 with a 1 and these do become twins 1571 and 1571. Thus the number of 4 digit numbers that can be formed from 1159 is half the number that can be formed from 1259.
I hope this helps,
Harley
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