puzzling se

115935.c

#include <algorithm>
#include <cstdio>
#include <iostream>
#include <numeric>
#include <set>
#include <vector>

using namespace std;
typedef long long LL;
typedef pair<int, int> pii;

#define forup(i, a, b) for (int i = (a); i < (b); ++i)
#define fordn(i, a, b) for (int i = (a); i > (b); --i)
#define rep(i, a) for (int i = 0; i < (a); ++i)

#define gi(x) scanf("%d", &x)
#define gl(x) cin >> x
#define gd(x) scanf("%lf", &x)
#define gs(x) scanf(" %s", x)

#define fs first
#define sc second

#define pb push_back
#define mp make_pair

const int inf = numeric_limits<int>::max();
const LL linf = numeric_limits<LL>::max();
const LL nlinf = numeric_limits<LL>::min();

const int max_n = 100010;

int arr[max_n];
vector<int> prime;
bool is_composite[max_n];

void sieve(int n) {
  fill(is_composite, is_composite + n, false);
  for (int i = 2; i < n; ++i) {
    if (!is_composite[i])
      prime.pb(i);
    for (int j = 0; j < prime.size() && i * prime[j] < n; ++j) {
      is_composite[i * prime[j]] = true;
      if (i % prime[j] == 0)
        break;
    }
  }
}

bool is_prime(int n) { return !is_composite[n]; }

bool is_topexp(int n, int x) {
  int base = 0;
  for (auto &i : prime) {
    if (x % i == 0) {
      base = i;
      break;
    }
  }
  int y = 1;
  while (y*base <= n) {
    y *= base;
  };

  if (x == y)
    return true;
  y /= base;
  if (x == y)
    return true;
  return false;
}

bool sat(int n, vector<int> a, vector<int> b) {
  for (auto &i : a) {
    // printf("%d:", i);
    int c = 0;
    for (auto &j : a) {
      if (i != j && gcd(i, j) > 1) {
        c++;
        if (c > 2) {
          printf("A %d\n", i);
          return false;
        }
      }
    }
  }
//   putchar(0xa);
  for (auto &i : b) {
    int c = 0;
    for (auto &j : a) {
      if (gcd(i, j) > 1) {
        c++;
      }
    }
    if (c < 3) {
      printf("B %d\n", i);
      return false;
    }
  }
  return true;
}

bool check(int n) {
  vector<int> a, b;
  forup(i, 1, n + 1) {
    if (i == 1 || is_prime(i) || is_topexp(n, i))
      a.pb(i);
    else
      b.pb(i);
  }
  return sat(n, a, b);
}

int main() {
  sieve(max_n);
  assert(is_topexp(36, 25));
  assert(is_topexp(9, 9));
  assert(is_topexp(8, 4));
  forup(i, 1, max_n) {
    // printf("%d\n", i);
    assert(check(i));
  }
}

91316.pl

:- use_module(library(clpfd)).

list_allperms(L, Ps) :- bagof(P, permutation(L,P), Ps).

f(X,Y,Z,R) :- R #= 10 * X + 11 * Y + 12 * Z.
fit(X,Y,Z) :- f(X,Y,Z,R), R #< 51.

fit_limit(L) :- nth0(0,L,X),nth0(1,L,Y),nth0(2,L,Z),fit(X,Y,Z).
fit_unique(L,R) :- nth0(0,L,X),nth0(1,L,Y),nth0(2,L,Z),f(X,Y,Z,R).

solution(X,Y,Z) :-
    X #>=0,
    Y #>=0,
    Z #>=0,
    list_allperms([X,Y,Z],L),
    maplist(fit_limit, L),
    maplist(fit_unique,L,R),
    all_distinct(R),
    label([X,Y,Z]),
    write(R).

91319.pl

:- use_module(library(clpfd)).

fit(X) :- X #>= 1, X #=< 7 .

n_fit(L,V) :- nth0(X1,L,V),nth0(Y1,L,V),X1 #\= Y1, abs(X1-Y1) #= (V+1).

n_six_fit(L,Base,Idx,Val) :- Y #= Base+Idx, nth0(Y,L,X), X #= Val.

count_fit(L) :- maplist(n_fit(L),[1,2,3,4,5,6,7]).

six_fit(L) :- nth0(X6,L,6),nth0(Y6,L,6), Y6 #> X6, Y6 #=< 13, X6 #=< 6,
              maplist(n_six_fit(L,X6),[1,2,3,4,5,6],N),
              is_set(N).

num([],0).
num([L|Ns],X) :- num(Ns,Y),length(Ns,P),X is L*(10**P) + Y.

solution(Num) :-
    maplist(fit,[M,N,O,P,Q,R,S,T,U,V,W,X,Y,S]),
    count_fit([M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z]),
    six_fit([M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z]),
    num([M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z],Num).


?- distinct(X,solution(X)).

91886.pl

:- use_module(library(clpfd)).

sudoku(Rows) :-
        length(Rows, 9), maplist(same_length(Rows), Rows),
        append(Rows, Vs), Vs ins 1..9,
        maplist(all_distinct, Rows),
        transpose(Rows, Columns),
        maplist(all_distinct, Columns),
        Rows = [As,Bs,Cs,Ds,Es,Fs,Gs,Hs,Is],
        blocks(As, Bs, Cs),
        blocks(Ds, Es, Fs),
        blocks(Gs, Hs, Is),
        nth0(0,As,D1),nth0(1,Bs,D2),nth0(2,Cs,D3),nth0(3,Ds,D4),nth0(4,Es,D5),nth0(5,Fs,D6),nth0(6,Gs,D7),nth0(7,Hs,D8),nth0(8,Is,D9),
        nth0(8,As,E1),nth0(7,Bs,E2),nth0(6,Cs,E3),nth0(5,Ds,E4),nth0(4,Es,E5),nth0(3,Fs,E6),nth0(2,Gs,E7),nth0(1,Hs,E8),nth0(0,Is,E9),
        nth0(1,Bs,F1),nth0(4,Bs,F2),nth0(7,Bs,F3),nth0(1,Es,F4),nth0(4,Es,F5),nth0(7,Es,F6),nth0(1,Hs,F7),nth0(4,Hs,F8),nth0(7,Hs,F9),
        all_distinct([D1,D2,D3,D4,D5,D6,D7,D8,D9]),
        all_distinct([E1,E2,E3,E4,E5,E6,E7,E8,E9]),
        all_distinct([F1,F2,F3,F4,F5,F6,F7,F8,F9]),
        nth0(3,As,K1_1),nth0(3,Cs,K1_2),nth0(0,Ds,K1_3),nth0(2,Ds,K1_4),K1_1 #\= F1,K1_2 #\= F1,K1_3 #\= F1,K1_4 #\= F1,
        nth0(2,As,K2_1),nth0(2,Cs,K2_2),nth0(6,As,K2_3),nth0(6,Cs,K2_4),nth0(3,Ds,K2_5),nth0(5,Ds,K2_6),K2_1 #\= F2,K2_2 #\= F2,K2_3 #\= F2,K2_4 #\= F2,K2_5 #\= F2,K2_6 #\= F2,
        nth0(6,As,K3_1),nth0(6,Cs,K3_2),nth0(6,Ds,K3_3),nth0(8,Ds,K3_4),K3_1 #\= F3,K3_2 #\= F3,K3_3 #\= F3,K3_4 #\= F3,
        nth0(3,Ds,K4_1),nth0(3,Fs,K4_2),nth0(0,Gs,K4_3),nth0(2,Gs,K4_4),nth0(0,Cs,K4_5),nth0(2,Cs,K4_6),K4_1 #\= F4,K4_2 #\= F4,K4_3 #\= F4,K4_4 #\= F4,K4_5 #\= F4,K4_6 #\= F4,
        nth0(3,Cs,K5_1),nth0(5,Cs,K5_2),nth0(2,Ds,K5_3),nth0(2,Fs,K5_4),nth0(6,Ds,K5_5),nth0(6,Fs,K5_6),nth0(3,Gs,K5_7),nth0(5,Fs,K5_8),K5_1 #\= F5,K5_2 #\= F5,K5_3 #\= F5,K5_4 #\= F5,K5_5 #\= F5,K5_6 #\= F5,K5_7 #\= F5,K5_8 #\= F5,
        nth0(5,Ds,K6_1),nth0(5,Fs,K6_2),nth0(6,Gs,K6_3),nth0(8,Gs,K6_4),nth0(6,Cs,K6_5),nth0(8,Cs,K6_6),K6_1 #\= F6,K6_2 #\= F6,K6_3 #\= F6,K6_4 #\= F6,K6_5 #\= F6,K6_6 #\= F6,
        nth0(0,Fs,K7_1),nth0(2,Fs,K7_2),nth0(3,Is,K7_3),nth0(3,Gs,K7_4),K7_1 #\= F7,K7_2 #\= F7,K7_3 #\= F7,K7_4 #\= F7,
        nth0(2,Gs,K8_1),nth0(2,Is,K8_2),nth0(6,Gs,K8_3),nth0(6,Is,K8_4),nth0(3,Fs,K8_5),nth0(5,Fs,K8_6),K8_1 #\= F8,K8_2 #\= F8,K8_3 #\= F8,K8_4 #\= F8,K8_5 #\= F8,K8_6 #\= F8,
        nth0(8,Fs,K9_1),nth0(6,Fs,K9_2),nth0(5,Gs,K9_3),nth0(5,Is,K9_4),K9_1 #\= F9,K9_2 #\= F9,K9_3 #\= F9,K9_4 #\= F9.
        

blocks([], [], []).
blocks([N1,N2,N3|Ns1], [N4,N5,N6|Ns2], [N7,N8,N9|Ns3]) :-
        all_distinct([N1,N2,N3,N4,N5,N6,N7,N8,N9]),
        blocks(Ns1, Ns2, Ns3).

problem(1,     [[8,2,1,4,7,9,_,_,6],
                [_,9,4,_,_,3,_,_,_],
                [_,_,3,_,_,_,9,1,_],
                [_,_,_,_,2,_,_,_,9],
                [_,_,9,3,_,_,_,_,_],
                [_,_,_,_,9,_,_,_,_],
                [_,_,_,9,_,7,_,_,_],
                [9,_,_,6,3,_,4,_,_],
                [3,_,_,_,_,_,1,9,_]]).

92024.pl

:- use_module(library(clpfd)).

sudoku(Rows) :-
        length(Rows, 9), maplist(same_length(Rows), Rows),
        append(Rows, Vs), Vs ins 1..9,
        maplist(all_distinct, Rows),
        transpose(Rows, Columns),
        maplist(all_distinct, Columns),
        Rows = [As,Bs,Cs,Ds,Es,Fs,Gs,Hs,Is],
        blocks(As, Bs, Cs),
        blocks(Ds, Es, Fs),
        blocks(Gs, Hs, Is),
        nth0(0,As,D1),nth0(1,Bs,D2),nth0(2,Cs,D3),nth0(3,Ds,D4),nth0(4,Es,D5),nth0(5,Fs,D6),nth0(6,Gs,D7),nth0(7,Hs,D8),nth0(8,Is,D9),
        nth0(8,As,E1),nth0(7,Bs,E2),nth0(6,Cs,E3),nth0(5,Ds,E4),nth0(4,Es,E5),nth0(3,Fs,E6),nth0(2,Gs,E7),nth0(1,Hs,E8),nth0(0,Is,E9),
        nth0(1,Bs,F1),nth0(4,Bs,F2),nth0(7,Bs,F3),nth0(1,Es,F4),nth0(4,Es,F5),nth0(7,Es,F6),nth0(1,Hs,F7),nth0(4,Hs,F8),nth0(7,Hs,F9),
        all_distinct([D1,D2,D3,D4,D5,D6,D7,D8,D9]),
        all_distinct([E1,E2,E3,E4,E5,E6,E7,E8,E9]),
        all_distinct([F1,F2,F3,F4,F5,F6,F7,F8,F9]),
        F3 #< F2,
        F2 #< F1,
        F1 #< F4,
        F4 #< F7,
        F7 #< F8,
        F8 #< F9,
        % F9 #< F6,
        F6 #< F3.
        % write(done).

blocks([], [], []).
blocks([N1,N2,N3|Ns1], [N4,N5,N6|Ns2], [N7,N8,N9|Ns3]) :-
        all_distinct([N1,N2,N3,N4,N5,N6,N7,N8,N9]),
        blocks(Ns1, Ns2, Ns3).

problem(1, [[5,7,2,_,_,9,_,3,1],
            [6,4,8,_,3,1,_,2,_],
            [9,1,3,_,_,_,_,_,_],
            [_,3,7,1,5,_,_,_,_],
            [_,5,6,_,9,_,3,1,8],
            [8,9,1,3,_,6,_,7,5],
            [1,2,5,9,_,_,7,6,3],
            [3,6,9,_,7,_,1,8,4],
            [7,8,4,6,1,3,_,_,2]]).

92053.py

from random import randint, sample
from collections import defaultdict

def cals():
    start_set = set()

    start_set.add(1)
    buf = ""
    rank = {}
    rank[1] = 1
    # rank[0] = 2
    while len(start_set) < 100:
        a = sample(start_set, 1)
        b = sample(start_set, 1)
        # print(a,b)
        # if a[0] > 5000 or b[0] > 5000:
        #     continue
        if 2020 in start_set:
            break
        start_set.add(a[0] + b[0])
        start_set.add(abs(a[0] - b[0]))
        start_set.add(a[0] * b[0])
        buf += "%d + %d = %d\n%d - %d = %d\n%d * %d = %d\n" % (a[0],b[0],a[0]+b[0],a[0],b[0],abs(a[0]-b[0]),a[0],b[0],a[0]*b[0])
        if (a[0] + b[0]) not in rank:
            rank[a[0] + b[0]] = max(rank[a[0]],rank[b[0]]) + 1
        if (a[0] * b[0]) not in rank:
            rank[a[0] * b[0]] = max(rank[a[0]],rank[b[0]]) + 1
        if abs(a[0] - b[0]) not in rank:
            rank[abs(a[0] - b[0])] = max(rank[a[0]],rank[b[0]]) + 1

    if 2020 in start_set:
        # print(start_set)
        # print(buf)
        # print(rank[2020])
        return (rank[2020],buf)
    else:
        return (None,None)


while True:
    x,y = cals()
    if x:
        print(x)
        if x < 8:
            print(y)

92224.pl

:- use_module(library(clpfd)).

forward(you, 240).
forward(jacky, 360).
forward(chris, 420).
forward(martha, 600).

backward(you, 120).
backward(jacky, 60).
backward(chris, 45).
backward(martha, 30).

moves(Ms) :- phrase(moves(state(0,[you,jacky,chris,martha],[])), Ms).

moves(state(T0,Ls0,Rs0)) -->
        { select(Player1, Ls0, Ls1), select(Player2, Ls1, Ls2),
          Player1 @< Player2,
          forward(Player1, Time1), forward(Player2, Time2),
          T1 #= T0 + max(Time1,Time2), T1 #< 1500 },
        [together(Player1,Player2,T1)],
        moves_(state(T1,Ls2,[Player1,Player2|Rs0])).

moves_(state(_,[],_))     --> [].
moves_(state(T0,Ls0,Rs0)) -->
        { select(Player, Rs0, Rs1),
          backward(Player, Time),
          T1 #= T0 + Time, T1 #< 1500 },
        [alone(Player,T1)],
        moves(state(T1,[Player|Ls0],Rs1)).

92260.py

from graphviz import Graph
from fractions import gcd
p1 = [9, 15, 21, 10, 7, 70]

G1 = Graph('G1', filename="Graph1")
edges = []
for i in p1:
    for j in p1:
        if i != j and gcd(i, j) > 1:
            edges.append((i, j))
edges = set([tuple(sorted(i)) for i in edges])
for edge in edges:
    G1.edge(str(edge[0]), str(edge[1]))
G1.view()
G1.save("G1.dot")
p2 = [9, 42, 21, 20, 35, 5]

G2 = Graph('G2', filename="Graph2")
edges = []
for i in p2:
    for j in p2:
        if i != j and gcd(i, j) > 1:
            edges.append((i, j))
edges = set([tuple(sorted(i)) for i in edges])
for edge in edges:
    G2.edge(str(edge[0]), str(edge[1]))
G2.view()
G2.save("G2.dot")

92402.pl

:- use_module(library(clpfd)).

median(Row, X) :-
    msort(Row, Sorted),
    nth0(1, Sorted, X).

solution(Rows) :-
    length(Rows, 3),
    maplist(same_length(Rows), Rows),
    append(Rows, Vs),
    permutation(Vs, [1, 2, 3, 4, 5, 6, 7, 8, 9]),
    transpose(Rows, Columns),
    maplist(median, Rows, RMedians),
    maplist(median, Columns, CMedians),
    append([RMedians, CMedians], AllMedians),
    all_distinct(AllMedians), writeln(Rows), writeln(CMedians), writeln(RMedians).

solve(1, [[_, _, _], [_, _, _], [_, _, _]]).

?-solve(1, X), solution(X), maplist(portray_clause, X).

se_43500776.pl

:- use_rendering(table,
		 [header(h('Name','Surname','L1','L2'))]).

interpreters(Is) :-
    length(Is,6),
    member(h(fran,french,_,_), Is),
    member(h(geraldine,german,_,_), Is),
    member(h(dudley,dutch,_,_), Is),
    member(h(spike,spanish,_,_), Is),
    member(h(polly,polish,_,_), Is),
    member(h(ron,romanian,_,_), Is),
    member(h(_,_,french,_), Is),member(h(_,_,_,french), Is),
    member(h(_,_,german,_), Is),member(h(_,_,_,german), Is),
    member(h(_,_,dutch,_), Is),member(h(_,_,_,dutch), Is),
    member(h(_,_,spanish,_), Is),member(h(_,_,_,spanish), Is),
    member(h(_,_,polish,_), Is),member(h(_,_,_,polish), Is),
    member(h(_,_,romanian,_), Is),member(h(_,_,_,romanian), Is),
    \+member(h(_,X,X,_), Is),
    \+member(h(_,Y,_,Y), Is),
    (member(h(spike,spanish,dutch,german), Is);member(h(spike,spanish,german,dutch), Is)),
    (member(h(_,_,dutch,polish), Is);member(h(_,_,polish,dutch), Is)),
    member(h(fran,french,E,F), Is),member(h(dudley,dutch,G,H), Is),E \= G, F \= G, E \= H, F \= H,
    member(h(dudley,dutch,I,J), Is), (member(h(_,I,_,french), Is);member(h(_,I,french,_), Is)), (member(h(_,J,_,french), Is);member(h(_,J,french,_), Is)),
    \+member(h(_,_,german,polish), Is),
    \+member(h(_,_,polish,german), Is),
    \+member(h(_,_,K,K), Is).

se_47927614.pl

:- use_module(library(clpfd)).

%   Of the shrine in Uchida and the temple built in 1645, one is sama takako and the other is okabe honzo.
%   The temple in Funai was built before takahashi
%   The temple in toyagi was built 120 years before the temple in usui
%   Hori takesi wasa built after sama takako



temples(Ts):-
    length(Ts,4),
    member(h(hori_takesi, _, _), Ts),
    member(h(okabe_honzo, _, _), Ts),
    member(h(sama_takako, _, _), Ts),
    member(h(takahashi, _, _), Ts),
    member(h(_, funai, _), Ts),
    member(h(_, toyagi, _), Ts),
    member(h(_, uchida, _), Ts),
    member(h(_, usui, _), Ts),
    member(h(_, _, 1525), Ts),
    member(h(_, _, 1585), Ts),
    member(h(_, _, 1645), Ts),
    member(h(_, _, 1705), Ts),
    member(h(takahashi, _, X), Ts), member(h(_, funai, Y), Ts), Y #< X,
    member(h(_, toyagi, Z), Ts), member(h(_, usui, W), Ts), Z + 120 #= W,
    member(h(sama_takako, _, U), Ts), member(h(hori_takesi, _, V), Ts), V #> U,
    (member(h(sama_takako,uchida,_), Ts),member(h(okabe_honzo,_,1645), Ts),\+member(h(okabe_honzo,uchida,_),Ts),\+member(h(sama_takako,_,1645), Ts));(\+member(h(sama_takako,uchida,_), Ts),\+member(h(okabe_honzo,_,1645), Ts),member(h(okabe_honzo,uchida,_),Ts),member(h(sama_takako,_,1645), Ts)).

se_58785006.pl

day(X) :- member(X,[m,t,w,thu,f,sat,sun]).

lie(m).
lie(t).
lie(w).

truth(X) :- \+lie(X).

next(A, B, Ls) :- append(_, [A,B|_], Ls).

next_day(sun,m).
next_day(X,Y) :- next(X,Y,[m,t,w,thu,f,sat,sun]).

solve(X) :-
    day(X),
    (truth(X),next_day(Y,X),lie(Y),next_day(X,T),next_day(T,U),next_day(U,V),lie(U),lie(V));
    (lie(X),next_day(Y,X),truth(Y),next_day(X,T),next_day(T,U),next_day(U,V),(truth(U);truth(V))).