Cinquante signes

Hello math-Fun, Some terminology – say we have an infinite square grid like this: – we put the integer 42 somewhere in a cell (we are not allowed to put more than one integer  per cell): – the cell 42 has 8 immediate neighbors – we give the name frame to the 8 cells forming this neighborhood (highlighted in yellow hereunder): – what is a rhyme in such a context? – say the sum of the 8 integers (that will form in the future the frame of 42) is k – we want k to end with the string 42 (the sum rhymes with 42 when k = 42, or 142, or 242, or 342, etc.) The goal W e want to amaze the audience by showing them a grid filled with numbers and then asking them to pick one at random. We show then that the sum of the eight neighbors of this number ends (graphically) with the chosen integer! The algorithm We start to fill the grid with a square spiral S centered on the integer 0 (zero); the constraint is to lexico-extend the spiral step by step with distinct integers rhyming with their frame. If w

Hello Gavin , It’s time to face some serious challenges!-) The idea —> We ask a bunch of kids to paint in red all the pairs of successive digits they can find in the seq S — but only if this pair is made of contiguous digits of opposite parity (like 1,4 or 7,2 or 0, 9);  —> the digits may belong to two different integers (after painting red the digits of the segment … 48 0 , 1 33 , 54 , … the black remaining digits will form 48., .33, .. );  —> once a pair is painted red, the kids do NOT iterate from there: the above segment [ … 48 0 , 1 33 , 54 , …]  does not become [ … 4 8 0 , 13 3 , 54 , …]  and this one doesn’t become fully red at the « next step » [ … 48 0 , 133 , 54 , …] as there are no successive such steps. —> the kids work SIMULTANEOUSLY, they start to paint S where they want — no one expects the result of someone else to proceed with the painting. That’s it! When the kids are finished, they make a step back and look at the seq: surprise, the black remainin