And So On And So On

If you change the order of these digits you can get 24 different numbers, for example 2547, 2574, 2745, …  Can you find all 24 different numbers made by using each of the digits 2, 4, 5, 7 just once?

How many of these numbers have 2 in the thousands place? How many have 2 in the hundreds place? How many have 2 in the tens place? How many have 2 in the units place?

Now find what these 24 four digit numbers add up to.
How many methods can you find for solving this problem?

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See the AIMSSEC Notes for Teachers

This problem is adapted from the NRICH task And So On and So On with permission of the University of Cambridge. All rights reserved.