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0b7acaf5ae |
@ -46,10 +46,10 @@ Use two half adders to construct a full adder.
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#solution([
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$
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s_1, c_1 &= "HA"(a, b) \
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s_2, c_2 &= "HA"(s_1, c_"in") \
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s_"out" &= s_2 \
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c_"out" &= "OR"(c_1, c_2)
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s_1, c_1 & = "HA"(a, b) \
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s_2, c_2 & = "HA"(s_1, c_"in") \
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s_"out" & = s_2 \
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c_"out" & = "OR"(c_1, c_2)
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$
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#v(2mm)
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@ -7,7 +7,7 @@
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#problem()
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Take any positive integer $n$. \
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Now, write it as sum of smaller positive integers: $n = a_1 + a_2 + ... a_k$ \
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Now, write it as sum of smaller positive integers: $n = a_1 + a_2 + ... a_k$ \
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Maximize the product $a_1 #sym.times a_2 #sym.times ... #sym.times a_k$
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@ -17,7 +17,9 @@ Maximize the product $a_1 #sym.times a_2 #sym.times ... #sym.times a_k$
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Of course, all $a_i$ should be greater than $1$. \
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Also, all $a_i$ should be smaller than four, since $x <= x(x-2)$ if $x >= 4$. \
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Thus, we're left with sequences that only contain 2 and 3. \
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#note([Note that two twos are the same as one four, but we exclude fours for simplicity.])
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#note(
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[Note that two twos are the same as one four, but we exclude fours for simplicity.],
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)
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#v(2mm)
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