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August 17, 2017 17:57
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SMT-LIB solution to the fish riddle
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; Copyright 2017 Google Inc. | |
; | |
; Licensed under the Apache License, Version 2.0 (the "License"); | |
; you may not use this file except in compliance with the License. | |
; You may obtain a copy of the License at | |
; | |
; https://www.apache.org/licenses/LICENSE-2.0 | |
; | |
; Unless required by applicable law or agreed to in writing, software | |
; distributed under the License is distributed on an "AS IS" BASIS, | |
; WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
; See the License for the specific language governing permissions and | |
; limitations under the License. | |
; This is a SMT-LIB solution to | |
; https://ed.ted.com/lessons/can-you-solve-the-fish-riddle-steve-wyborney. | |
; There are fish tanks and sharks. | |
(declare-const tanks-a Int) | |
(declare-const tanks-b Int) | |
(declare-const tanks-c Int) | |
(declare-const sharks-a Int) | |
(declare-const sharks-b Int) | |
(declare-const sharks-c Int) | |
(assert (>= tanks-a 0)) | |
(assert (>= tanks-b 0)) | |
(assert (>= tanks-c 0)) | |
(assert (>= sharks-a 0)) | |
(assert (>= sharks-b 0)) | |
(assert (>= sharks-c 0)) | |
; There are fish in the tanks. | |
(declare-const fish-per-tank Int) | |
(assert (>= fish-per-tank 0)) | |
(define-fun tanks () Int (+ tanks-a tanks-b tanks-c)) | |
(define-fun fish () Int (* fish-per-tank tanks)) | |
(define-fun sharks () Int (+ sharks-a sharks-b sharks-c)) | |
(define-fun total-creatures () Int (+ fish sharks)) | |
; There are 50 creatures total. | |
(assert (= total-creatures 50)) | |
; Each sector has between 1 and 7 sharks. | |
(assert (<= 1 sharks-a 7)) | |
(assert (<= 1 sharks-b 7)) | |
(assert (<= 1 sharks-c 7)) | |
; No two sectors have the same number of sharks. | |
(assert (not (= sharks-a sharks-b))) | |
(assert (not (= sharks-b sharks-c))) | |
(assert (not (= sharks-a sharks-c))) | |
; There are 13 or fewer tanks. | |
(assert (<= tanks 13)) | |
; We know some stuff about sectors alpha and beta. | |
(assert (= sharks-a 2)) | |
(assert (= tanks-a 4)) | |
(assert (= sharks-b 4)) | |
(assert (= tanks-b 2)) | |
(check-sat) | |
(get-model) |
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