Tool to search path in a number pyramid. Path search in a pyramid triangle allows to find the shortest path or the longest path by traversing the graph (tree) from the root to its leaves or from the bottom to the top.

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Go through the pyramid (or the triangle) from top to bottom, adding values that gave a the smallest total respecting a single rule : only go to one of the two numbers immediately below.

Example:...5... ..4.8.. .9.5.2. 1.2.7.6 2nd line: 5+4=9 or 5+8=13, choose the lowest, the path 5->4. 3rd line: 4+9=13 or 4+5=9, choose the lowest, the path 4->5. 4th line: 5+2=7 or 5+7=12, choose the lowest, the path 5->2. Finally, the shortest path route is (from top to bottom) 5->4->5->2 (which is 16 long) or 2->5->4->5 (from bottom to top)

How to find the longest path?

Go through the pyramid from top to bottom, as for the shortest path, but by adding values that gave the highest total.

How to count possible paths?

Total number of path $ N $ in a pyramid of height $ H $ is given by the formula : $$ N = 2^{H-1} $$

Source code

dCode retains ownership of the online 'Path Search in a Pyramid Triangle' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Path Search in a Pyramid Triangle' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Path Search in a Pyramid Triangle' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Path Search in a Pyramid Triangle' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Need Help ?

Please, check our dCode Discord community for help requests! NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Path Search in a Pyramid Triangle' tool, so feel free to write! Thank you!

Thanks to your feedback and relevant comments, dCode has developed the best 'Path Search in a Pyramid Triangle' tool, so feel free to write! Thank you!