Data update

Task/Babbage-problem/Pluto/babbage-problem.pluto

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+--[[
+    The answer must be an even number and it can't be less than the square root of 269,696.
+    So, if we start from that, keep on adding 2 and squaring it we'll eventually find the answer.
+    However, we can skip numbers which don't end in 4 or 6 as their squares can't end in 6.
+]]
+
+local fmt  = require "fmt"        -- this enables us to format numbers with thousand separators
+local start = math.sqrt(269696)   -- get the square root of the starting value
+start = math.ceil(start)          -- get the next integer higher than (or equal to) the square root
+start = math.ceil(start / 2) * 2  -- if it's odd, use the next even integer
+local i = start                   -- assign it to a variable 'i' for use in the following loop
+while true do                     -- loop indefinitely till we find the answer
+    local sq = i * i              -- get the square of 'i'
+    local last6 = sq % 1000000    -- get its last 6 digits by taking the remainder after division by a million
+    if last6 == 269696 then       -- if those digits are 269696, we're done and can print the result
+        fmt.print($"The lowest number whose square ends in 269,696 is %,s.", i)
+        fmt.print($"Its square is %,s.", sq)
+        break                     -- break from the loop and end the program
+    end
+    if i % 10 == 6 then           -- get the last digit by taking the remainder after division by 10
+        i += 8                    -- if the last digit is 6 add 8 (to end in 4)
+    else
+        i += 2                    -- otherwise add 2
+    end
+end