This Tower of Brahma is the classic puzzle game Tower Of Hanoi a.k.a. The problem of Benares Temple or Lucas' Tower
Animation by André Karwath via Creative Commons
This game was invented by the mathematician Lucas in the 1880s - it is a an old game. Lucas set the game with the Brahmans of Tonkin, and Hanoi was the capital of Tonkin. Hence the varying names given to different versions of the game
As is the tradition, many versions were created for early home computers, and this one is by the Danish company Scan-Bit-Software. It is a simply presented program with a nice animation of moving a disc from one rod to the next. But simple doesn't mean non-challenging. There is a lot of strategy involved, especially when you get to nine discs. Start with 3 discs until you get the sense of it
It is a pure BASIC program, using only the block graphics, so at the source-code level it is completely compatible with the ZX81. However, the binary format (on cassette tape) is for the Lambda 8300 type machines only. Here is a port to ZX81 translated into English -- which as usual will load into Lambdas that have the "READY" ROM
Instructions: press the keys "12" and "ENTER" to move a disc from needle 1 to needle 2 and so forth; continue until all the discs have been transferred to the center needle
The original Danish version at Software Preservation has the cassette inlay instructions. Thanks, kolbeck!