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Mind boggling card trick: Difference between revisions
→{{header|Lua}}: added Lua solution
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So the asssertion is correct!
</pre>
=={{header|Lua}}==
<lang lua>-- support:
function T(t) return setmetatable(t, {__index=table}) end
table.range = function(t,n) local s=T{} for i=1,n do s[i]=i end return s end
table.map = function(t,f) local s=T{} for i=1,#t do s[i]=f(t[i]) end return s end
table.filter = function(t,f) local s=T{} for i=1,#t do if f(t[i]) then s[#s+1]=t[i] end end return s end
table.clone = function(t) local s=T{} for k,v in ipairs(t) do s[k]=v end return s end
table.head = function(t,n) local s=T{} n=n>#t and #t or n for i = 1,n do s[i]=t[i] end return s end
table.tail = function(t,n) local s=T{} n=n>#t and #t or n for i = 1,n do s[i]=t[#t-n+i] end return s end
table.append = function(t,v) local s=t:clone() for i=1,#v do s[#s+1]=v[i] end return s end
table.shuffle = function(t) for i=#t,2,-1 do local j=math.random(i) t[i],t[j]=t[j],t[i] end return t end -- inplace!
-- task:
function cardtrick()
-- 1.
local deck = T{}:range(52):map(function(v) return v%2==0 and "B" or "R" end):shuffle()
print("1. DECK : " .. deck:concat())
-- 2. (which guarantees the outcome)
local bpile, rpile, discs = T{}, T{}, T{}
local xpile = {B=bpile, R=rpile}
while #deck>0 do
local card, next = deck:remove(), deck:remove()
xpile[card]:insert(next)
discs:insert(card)
end
print("2. BLACK PILE: " .. bpile:concat())
print("2. RED PILE : " .. rpile:concat())
print("2. DISCARDS : " .. discs:concat())
-- 3. (which cannot change the outcome)
local x = math.random(0, math.min(#bpile, #rpile))
local btake, rtake = T{}, T{}
for i = 1, x do
btake:insert((bpile:remove(math.random(#bpile))))
rtake:insert((rpile:remove(math.random(#rpile))))
end
print("3. SWAPPING X: " .. x)
print("3. BLACK SWAP: keep:" .. bpile:concat() .. " take:" .. btake:concat())
print("3. RED SWAP : keep:" .. rpile:concat() .. " take:" .. rtake:concat())
bpile, rpile = bpile:append(rtake), rpile:append(btake)
print("3. BLACK PILE: " .. bpile:concat())
print("3. RED PILE : " .. rpile:concat())
-- 4. ("proving" that which was guaranteed earlier)
local binb, rinr = bpile:filter(function(v) return v=="B" end), rpile:filter(function(v) return v=="R" end)
print("4. BLACK PILE: contains " .. #binb .. " B's")
print("4. RED PILE : contains " .. #rinr .. " R's")
print(#binb==#rinr and "VERIFIED" or "NOT VERIFIED")
print()
end
-- demo:
math.randomseed(os.time())
for i = 1,3 do cardtrick() end</lang>
{{out}}
<pre>1. DECK : RBBBRBRBRBBBBRRRRBRBBBRRBRRBRRBRBBRRBBRRBBRRRBBRBRBR
2. BLACK PILE: RBBBRBRRBRRRBR
2. RED PILE : BBBRRRBRBRRB
2. DISCARDS : RRRBRBRBRBRRBRRBBBRRBBBBBB
3. SWAPPING X: 3
3. BLACK SWAP: keep:RBBRBRRRRBR take:BBR
3. RED SWAP : keep:BBRRBRBRR take:RBB
3. BLACK PILE: RBBRBRRRRBRRBB
3. RED PILE : BBRRBRBRRBBR
4. BLACK PILE: contains 6 B's
4. RED PILE : contains 6 R's
VERIFIED
1. DECK : BRBBRRRRRBRBBRRBRRRRRBRBRBBBBBBRRRRBBRBBRBBRRBBBRBBR
2. BLACK PILE: RBRRBRBBRRRRRRB
2. RED PILE : BBBRBRRBRRB
2. DISCARDS : RBBBRBBRBRRBBBBBRRBRBBRRBR
3. SWAPPING X: 1
3. BLACK SWAP: keep:RRRBRBBRRRRRRB take:B
3. RED SWAP : keep:BBBRBRBRRB take:R
3. BLACK PILE: RRRBRBBRRRRRRBR
3. RED PILE : BBBRBRBRRBB
4. BLACK PILE: contains 4 B's
4. RED PILE : contains 4 R's
VERIFIED
1. DECK : BBRRRBBBBRBBRBBBRBRRRRRRBBRRRBRRBRRRRBRBBBRBBBBRBRBR
2. BLACK PILE: BRBRRRBRBRBBRB
2. RED PILE : BBBRBRRRRRBR
2. DISCARDS : RRRBBBBBRRRBRBRRRBBBBRBBRB
3. SWAPPING X: 5
3. BLACK SWAP: keep:BBRBRBBRB take:RBRRR
3. RED SWAP : keep:BRBRRBR take:BRRBR
3. BLACK PILE: BBRBRBBRBBRRBR
3. RED PILE : BRBRRBRRBRRR
4. BLACK PILE: contains 8 B's
4. RED PILE : contains 8 R's
VERIFIED</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
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