Solution to Rack Your Brain

This is the only solution, except that you may reverse the arrangement from left to right.

For more about this puzzle, see:

• Martin Gardner, Penrose Tiles to Trapdoor Ciphers (New York, W. H. Freeman, 1989; Washington, Mathematical Association of America, 1996; Cambridge, Cambridge University Press, 1997), Chapter 9;
• Gerard J. Chang, M. C. Hu, K. W. Lih, and T. C. Shieh, Exact Difference Triangles, Bulletin of the Institute of Mathematics, Academica Sinica, Old Series 5 (1977), No. 1, 191–197;
• Brian Chen, Yunhao Fu, Andy Liu, George Sicherman, Herbert Taylor, and Po-Sheng Wu, Triangles of Absolute Differences, in Thane Plambeck and Tomas Rokicki (eds.), Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers, Providence, R.I., MAA Press, 2020 (AMS / MAA Spectrum, v. 100), 115–124.