Numbers which can be computed with the same figure / published by https://github.com/dacr/code-examples-manager #395ba7b7-e618-4dbd-9bbf-3681c61a1762/9a7bf2f6fc79064ae096772880c6709062046a16

math-computes-with-same-number.sc

// summary : Numbers which can be computed with the same figure
// keywords : scala, math, challenge, @testable
// publish : gist
// authors : David Crosson
// license : Apache NON-AI License Version 2.0 (https://raw.githubusercontent.com/non-ai-licenses/non-ai-licenses/main/NON-AI-APACHE2)
// id : 395ba7b7-e618-4dbd-9bbf-3681c61a1762
// created-on : 2020-03-04T21:12:24Z
// managed-by : https://github.com/dacr/code-examples-manager
// run-with : scala-cli $file

// ---------------------
//> using scala  "3.1.1"
//> using dep "org.scalatest::scalatest:3.2.10"
// ---------------------
import org.scalatest._,flatspec._,matchers._
import scala.math._

type Solution=(Double,String)

//def fact(n:Long):Long = {
//    if (n==0L) 1L
//    else n*fact(n-1L)
//}

def fact(n:Long):Long = {
  @annotation.tailrec
  def worker(cn:Long, acc:Long):Long = {
    if (cn==0) acc
    else worker(cn-1, acc*cn)
  }
  worker(n, 1L)
}

/**
 * Find all computable numbers using the same digit the given number of time.
 *
 * Usable operations are : !, /, +, -, *, ^
 * @param figure which figure to use for all computes
 * @param count  how many figure we can use
 * @return found solutions
 */
def searchComputableFrom(figure: Int, count: Int): Set[Solution] = {
  val maxDepth=10
  def worker(currentValue: Double, currentCount: Int, proof:String, depth:Int): Set[Solution] = {
      val newdepth=depth+1
      if (currentCount==count) Set(currentValue->proof)
      else if (currentCount>count || depth>=maxDepth) Set()
      else if (currentCount==0) {
          worker(figure, currentCount+1, s"$figure",newdepth)++
          worker(fact(figure), currentCount+1, s"$figure!",newdepth)
      } else {
          worker(currentValue+figure, currentCount+1, s"$proof+$figure",newdepth)++
          worker(currentValue-figure, currentCount+1, s"$proof-$figure",newdepth)++
          worker(currentValue*figure, currentCount+1, s"($proof)*$figure",newdepth)++
          worker(currentValue/figure, currentCount+1, s"($proof)/$figure",newdepth)++
          worker(figure/currentValue, currentCount+1, s"$figure/($proof)",newdepth)++
          worker(pow(currentValue, figure), currentCount+1, s"($proof)^$figure",newdepth)++
          worker(pow(figure,currentValue), currentCount+1, s"$figure^($proof)",newdepth)++
          worker(fact(currentValue.toLong), currentCount, s"($proof)!",newdepth)
      }
  }
  worker(0, 0, "",0)
}


object MathChallengeTest extends AnyFlatSpec with should.Matchers {
  "searchComputableFrom" should "return the right results" in {
    searchComputableFrom(1, 1) shouldBe Set(
      1 -> "1!"
    )
    searchComputableFrom(1, 2) shouldBe Set(
      0 -> "1!-1!",
      0 -> "1-1",
      0 -> "1!-1",
      0 -> "1-1!",
      1 -> "1^1",
      1 -> "1/1",
      1 -> "1*1",
      2 -> "1!+1!",
      2 -> "1+1",
      2 -> "1!+1",
      2 -> "1+1!",
    )
  }

}

MathChallengeTest.execute()