Download The letters of EAT can be rearranged to become TEA

 This brainteaser was written by Derrick Niederman. The letters of EAT can be rearranged to become TEA by moving the third letter (T) to the first position and by moving the other letters one position to the right. This process could be described as 1→2, 2→3, 3→1. When this same process is applied again, then TEA becomes ATE. Similarly, the process 1→3, 2→2, 3→1, 4→4 will convert TONE to NOTE. When the process is applied again, NOTE returns to TONE. (Not very interesting, is it?) Your challenge begins with the five letters A, E, M, S, and T. Use them to form a common English word. Then, rearrange the letters to form a second common English word. Finally, apply the same process of rearrangement to form a third common English word. Can you do it? Resources for Teaching Math
© 2009 National Council of Teachers of Mathematics, Inc.
http://illuminations.nctm.org
Solution: MATES→STEAM→MEATS using the process 1→5, 2→4, 3→2, 4→3, 5→1. Five different words can be formed from the letters A, E, M, S, and T: MATES, MEATS, STEAM, TAMES, and TEAMS. Finding the solution then involves trial‐and‐error. Applying the process 1→5, 2→4, 3→2, 4→3, 5→1 will convert MATES to STEAM (uh, just the word steam, not actual steam), and when applied again, it will convert STEAM to MEATS (again, not literally). A visual representation of this process is shown below. It’s quite simple to exchange two letters, as in MEATS to TEAMS, and then go back again, but the problem required three different words. Resources for Teaching Math
© 2009 National Council of Teachers of Mathematics, Inc.
http://illuminations.nctm.org