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== Zeros == Have you ever wished you could count the number of zero digits in a long number like Rainman? by William Stein and Sequoia Lefthand {{attachment:zeros.png}} {{{#!sagecell import random def init(): global B,Br,n,round,tm,t,v B = 40 Br = 15 n = 1 round = 0 tm = 0 t = walltime() init() print "<html><h1 align=center>Zeros</h1></html>" print "<html><h2 align=center><font color='blue'>How many zeros?</font></h2></html>" @interact def zeros(a=("",selector(buttons=True, nrows=1, values=['Reset'] + [1..B], default=1))): if a == 'Reset': init() print "<html><center>" global B,Br,n,round,tm,t,v if a == n: if round > 0: print "<font size=+3 color='red'>RIGHT</font>" r = walltime() - t tm += r round += 1 t = walltime() while True: n2 = random.randrange(1,Br) if n2 != n: n = n2 break if Br < B: Br += 2 elif round > 0: print "<font size=+2 color='blue'>Wrong. Try again...</font>" print "</center>" print "<font size=+%s color='#333'>"%random.randrange(-2,5) print ' '*random.randrange(20) + '0'*n print "</font>" if round > 0: print "<br><br><center>Score: %s rounds, Average time: %.1f seconds</center>"%( round, float(tm)/round) print "</html>" }}} |
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| {{{ | {{{#!sagecell |
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| Play nim against a perfect oponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. | Play nim against a perfect opponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. |
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| {{{ | {{{#!sagecell |
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| {{{ nim=[1,3,5,7] |
{{{#!sagecell nim=[1,3,5,6] |
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| def _(heap=input_box(default=1), amount=input_box(default=0), auto_update=False ): | def _(heap=selector(range(len(nim)), buttons=True), amount=selector(range(max(nim)+1), buttons=True), auto_update=False): |
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| return | |
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| if max(nim)==0: print 'You win' return |
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| myheap=min(heap_number for heap_number, heap_size in enumerate(heap_size) if heap_size>0) | myheap=min(heap_number for heap_number, heap_size in enumerate(nim) if heap_size>0) myamount=1 |
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| if max(nim)==0: print 'I win' else: print 'Please move again' |
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| print 'Please choose a heap and the amount to substract from that heap' | print 'Choose a heap and the amount to substract from that heap' |
Sage Interactions - Games and Diversions
goto interact main page
Zeros
Have you ever wished you could count the number of zero digits in a long number like Rainman?
by William Stein and Sequoia Lefthand
xxxxxxxxxximport randomdef init(): global B,Br,n,round,tm,t,v B = 40 Br = 15 n = 1 round = 0 tm = 0 t = walltime() init() print "<html><h1 align=center>Zeros</h1></html>"print "<html><h2 align=center><font color='blue'>How many zeros?</font></h2></html>" def zeros(a=("",selector(buttons=True, nrows=1, values=['Reset'] + [1..B], default=1))): if a == 'Reset': init() print "<html><center>" global B,Br,n,round,tm,t,v if a == n: if round > 0: print "<font size=+3 color='red'>RIGHT</font>" r = walltime() - t tm += r round += 1 t = walltime() while True: n2 = random.randrange(1,Br) if n2 != n: n = n2 break if Br < B: Br += 2 elif round > 0: print "<font size=+2 color='blue'>Wrong. Try again...</font>" print "</center>" print "<font size=+%s color='#333'>"%random.randrange(-2,5) print ' '*random.randrange(20) + '0'*n print "</font>" if round > 0: print "<br><br><center>Score: %s rounds, Average time: %.1f seconds</center>"%( round, float(tm)/round) print "</html>"
Queens on board
An interaction to play with the problem of placing eight queens on a board so that they do not threaten each other. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. by Pablo Angulo
xxxxxxxxxxqueens=[]opciones=['Clean board', 'Add queen', 'Remove queen' ]def _(queen=input_box(default=(0,0)), opcion=selector(opciones, buttons=True), auto_update=False ): global queens if opcion=='Clean board': queens=[] elif opcion=='Add queen': if queen not in queens: queens.append(queen) else: queens.remove(queen) board=matrix(ZZ,8,8) for x in range(8): for y in range(8): board[x,y]=(x+y)%2*7 for x,y in queens: for i in range(8): if i!=y: board[x,i]=1+(x+i)%2*5 if i!=x: board[i,y]=1+(i+y)%2*5 for i in range(-min(x,y),min(8-x,8-y)): if i!=0: board[x+i,y+i]=1+(x+y)%2*5 for i in range(max(-x,y-7),min(8-x,y+1)): if i!=0: board[x+i,y-i]=1+(x+y)%2*5 for x,y in queens: if ( board[x,y]==1 or board[x,y]==6 ): print 'Queen at (%d,%d) is threatened by another queen'%(x,y) board[x,y]=4 else: board[x,y]=3 show(matrix_plot(board, cmap='Oranges' ))
Nim
Play nim against a perfect opponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. by Pablo Angulo
xxxxxxxxxx#El juego del nimdef game_repr(heap_sizes): return '\n'.join('%d:'%i+'*'*n for i,n in enumerate(heap_sizes))def bitlist2number(bitlist): return int('0'+''.join([str(bit) for bit in reversed(bitlist)]),2)def move_nim(heap_sizes): '''Given a nim game, returns the next move (heap and amount) ''' all_digits=[n.bits() for n in heap_sizes] N=max(len(l) for l in all_digits) digi=[0]*N for l in all_digits: for i in range(len(l)): digi[i]+=l[i] digi2=[digi[i]%2 for i in range(len(digi))] if max(digi2)==0:raise Exception("I cannot win!") maxInd=max(i for i in range(N) if digi2[i]) heap=min(i for i in range(len(heap_sizes)) if len(all_digits[i])>maxInd and all_digits[i][maxInd]>0) localbits=heap_sizes[heap].bits()[0:maxInd] globalbits=digi2[0:maxInd] correction=bitlist2number( [b2 if b2 and not b1 else 0 for b1,b2 in zip(localbits,globalbits)] ) - bitlist2number( [b2 if b2 and b1 else 0 for b1,b2 in zip(localbits,globalbits)] ) amount=2^maxInd -correction return (heap,amount)
xxxxxxxxxxnim=[1,3,5,6]def _(heap=selector(range(len(nim)), buttons=True), amount=selector(range(max(nim)+1), buttons=True), auto_update=False): global nim if max(nim)==0: print 'You have lost' return else: print 'Try to take the last item' if heap>=0 and 0<amount<=nim[heap]: print 'Previous situation:' print game_repr(nim) nim[heap]-=amount print 'Your move:' print game_repr(nim) if max(nim)==0: print 'You win' return print 'My move:' try: myheap,myamount=move_nim(nim) except: #cannot win, choose arbitrarily myheap=min(heap_number for heap_number, heap_size in enumerate(nim) if heap_size>0) myamount=1 nim[myheap]-=myamount print game_repr(nim) if max(nim)==0: print 'I win' else: print 'Please move again' else: print 'Choose a heap and the amount to substract from that heap' print game_repr(nim)