下の図のように○と×をある規則にしたがって並べていくとき

○×○○××○○○××××○○○○××××××××○・・・

(1)最初から数えて50番目は○×どちら？
(2)はじめて×の数の総和が○の数の総和の２倍になるのは、最初から数えて何番目？
　また、次に×の数の総和が○の総和の２倍になるのは、最初から数えて何番目？
(3)×の数の総和が○の数の総和の２倍になるのは、全部で何回起こるか。

新高２の学校春課題より抜粋。
ただ解いても面白くないので、練習がてら、スクリプトで解決。

turn,n,o,x,so,sx,ans,q1,q2a,q2b,q3=0,0,0,0,0,0,"","?",0,0,0
for t1 in range(18):
    turn+=1
    for t2 in range(turn):
        n+=1
        o+=1
        so+=1
        ans+="o"
        # print("[ ","turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," n=",n," ]",sep="")  # 途中を見たい人用
        if(n==50):
            q1="o"
            print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q1:gotcha!!\n[ ",ans," ]\n",sep="")
        if(sx==so*2):
            q3+=1
            if(q2a==0):q2a=n
            elif(q2b==0):q2b=n
            print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q2:gotcha!!\n[ ",ans," ]\n",sep="")
    for t3 in range(2**(turn-1)):
        n+=1
        x+=1
        sx+=1
        ans+="x"
        # print("[ ","turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," n=",n," ]",sep="")  # 途中を見たい人用
        if(n==50):
            q1="x"
            print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q1:gotcha!!\n[ ",ans," ]\n",sep="")
        if(sx==so*2):
            q3+=1
            if(q2a==0):q2a=n
            elif(q2b==0):q2b=n
            print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q2:gotcha!!\n[ ",ans," ]\n",sep="")
    # print(ans)  # xがずらりと表示されるだけになってしまうので注意。
    print("["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ]"," <<< turn(",turn,") is done.",sep="")
    o,x=0,0

turn,n,o,x,so,sx,ans,q1,q2a,q2b,q3=0,0,0,0,0,0,"","?",0,0,0

for t1 in range(18):

turn+=1

for t2 in range(turn):

n+=1

o+=1

so+=1

ans+="o"

# print("[ ","turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," n=",n," ]",sep="") # 途中を見たい人用

if(n==50):

q1="o"

print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q1:gotcha!!\n[ ",ans," ]\n",sep="")

if(sx==so*2):

q3+=1

if(q2a==0):q2a=n

elif(q2b==0):q2b=n

print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q2:gotcha!!\n[ ",ans," ]\n",sep="")

for t3 in range(2**(turn-1)):

n+=1

x+=1

sx+=1

ans+="x"

# print("[ ","turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," n=",n," ]",sep="") # 途中を見たい人用

if(n==50):

q1="x"

print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q1:gotcha!!\n[ ",ans," ]\n",sep="")

if(sx==so*2):

q3+=1

if(q2a==0):q2a=n

elif(q2b==0):q2b=n

print("\n","["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ] <<< Q2:gotcha!!\n[ ",ans," ]\n",sep="")

# print(ans) # xがずらりと表示されるだけになってしまうので注意。

print("["," n=",n," turn=",turn," o=",o," x=",x," S(o)=",so," S(x)=",sx," Q1=",q1," Q2first=",q2a," Q2second=",q2b," Q3=",q3," ]"," <<< turn(",turn,") is done.",sep="")

o,x=0,0

結果
>>python 20210403.py
[ n=2 turn=1 o=1 x=1 S(o)=1 S(x)=1 Q1=? Q2first=0 Q2second=0 Q3=0 ] <<< turn(1) is done.
[ n=6 turn=2 o=2 x=2 S(o)=3 S(x)=3 Q1=? Q2first=0 Q2second=0 Q3=0 ] <<< turn(2) is done.
[ n=13 turn=3 o=3 x=4 S(o)=6 S(x)=7 Q1=? Q2first=0 Q2second=0 Q3=0 ] <<< turn(3) is done.
[ n=25 turn=4 o=4 x=8 S(o)=10 S(x)=15 Q1=? Q2first=0 Q2second=0 Q3=0 ] <<< turn(4) is done.

[ n=45 turn=5 o=5 x=15 S(o)=15 S(x)=30 Q1=? Q2first=45 Q2second=0 Q3=1 ] <<< Q2:gotcha!!
[ oxooxxoooxxxxooooxxxxxxxxoooooxxxxxxxxxxxxxxx ]

[ n=46 turn=5 o=5 x=16 S(o)=15 S(x)=31 Q1=? Q2first=45 Q2second=0 Q3=1 ] <<< turn(5) is done.

[ n=50 turn=6 o=4 x=0 S(o)=19 S(x)=31 Q1=o Q2first=45 Q2second=0 Q3=1 ] <<< Q1:gotcha!!
[ oxooxxoooxxxxooooxxxxxxxxoooooxxxxxxxxxxxxxxxxoooo ]

[ n=63 turn=6 o=6 x=11 S(o)=21 S(x)=42 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< Q2:gotcha!!
[ oxooxxoooxxxxooooxxxxxxxxoooooxxxxxxxxxxxxxxxxooooooxxxxxxxxxxx ]

[ n=84 turn=6 o=6 x=32 S(o)=21 S(x)=63 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(6) is done.
[ n=155 turn=7 o=7 x=64 S(o)=28 S(x)=127 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(7) is done.
[ n=291 turn=8 o=8 x=128 S(o)=36 S(x)=255 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(8) is done.
[ n=556 turn=9 o=9 x=256 S(o)=45 S(x)=511 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(9) is done.
[ n=1078 turn=10 o=10 x=512 S(o)=55 S(x)=1023 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(10) is done.
[ n=2113 turn=11 o=11 x=1024 S(o)=66 S(x)=2047 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(11) is done.
[ n=4173 turn=12 o=12 x=2048 S(o)=78 S(x)=4095 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(12) is done.
[ n=8282 turn=13 o=13 x=4096 S(o)=91 S(x)=8191 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(13) is done.
[ n=16488 turn=14 o=14 x=8192 S(o)=105 S(x)=16383 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(14) is done.
[ n=32887 turn=15 o=15 x=16384 S(o)=120 S(x)=32767 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(15) is done.
[ n=65671 turn=16 o=16 x=32768 S(o)=136 S(x)=65535 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(16) is done.
[ n=131224 turn=17 o=17 x=65536 S(o)=153 S(x)=131071 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(17) is done.
[ n=262314 turn=18 o=18 x=131072 S(o)=171 S(x)=262143 Q1=o Q2first=45 Q2second=63 Q3=2 ] <<< turn(18) is done.

26万2314番目まで調べさせました。
○の総数が171個、×の総数が26万2143個でした。
○の総数を二倍した程度で×の総数に追いつくことはこの後ないでしょう。
というわけでQ3の答えは２個でいいでしょう。

isshinsemi

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