Initial data commit

Task/Babbage-problem/Racket/babbage-problem.rkt

@@ -0,0 +1,48 @@
+;; Text from a semicolon to the end of a line is ignored
+;; This lets the racket engine know it is running racket
+#lang racket
+
+;; “define” defines a function in the engine
+;; we can use an English name for the function
+;; a number ends in 269696 when its remainder when
+;; divided by 1000000 is 269696 (we omit commas in
+;; numbers... they are used for another reason).
+(define (ends-in-269696? x)
+  (= (remainder x 1000000) 269696))
+
+;; we now define another function square-ends-in-269696?
+;; actually this is the composition of ends-in-269696? and
+;; the squaring function (which is called “sqr” in racket)
+(define square-ends-in-269696? (compose ends-in-269696? sqr))
+
+;; a for loop lets us iterate (it’s a long Latin word which
+;; Victorians are good at using) over a number range.
+;;
+;; for/first go through the range and break when it gets to
+;; the first true value
+;;
+;; (in-range a b) produces all of the integers from a (inclusive)
+;; to b (exclusive). Because we know that 99736² ends in 269696,
+;; we will stop there. The add1 is to make in-range include 99736
+;;
+;; we define a new variable, so that we can test the verity of
+;; our result
+(define first-number-that-when-squared-ends-in-269696
+(for/first ((i ; “i” will become the ubiquetous looping variable of the future!
+             (in-range 1 (add1 99736)))
+            ; when returns when only the first one that matches
+            #:when (square-ends-in-269696? i))
+  i))
+
+;; display prints values out; newline writes a new line (otherwise everything
+;; gets stuck together)
+(display first-number-that-when-squared-ends-in-269696)
+(newline)
+(display (sqr first-number-that-when-squared-ends-in-269696))
+(newline)
+(newline)
+(display (ends-in-269696? (sqr first-number-that-when-squared-ends-in-269696)))
+(newline)
+(display (square-ends-in-269696? first-number-that-when-squared-ends-in-269696))
+(newline)
+;; that all seems satisfactory