Skripta Sbírka Matematika 3

06a105a99a104 a112a111a163a101a116 a106a101
n!
n1!·n2!···nk! .
a80a176a237a107a108a97a100 a49a46a57 a77a225a109a101 a98a97a108a237a163a101a107 a51a50 a114a183a122a110a253a99a104 a107a97a114a101a116a46 a72a114a225a163 a100a111a115a116a97a110a101 a53 a107a97a114a101a116a46 a75a111a108a105a107 a106a101 a109a111a186a110a111a115a116a237 a112a114a111
a116a117a116a111 a112a165a116a105a99a105a63 a40a78a101a122a225a108a101a186a237 a110a97 a116a111a109a44 a118 a106a97a107a233a109 a112a111a176a97a100a237 a98a121a108a121 a107a97a114a116a121 a114a111a122a100a225a110a121a46 a90a225a108a101a186a237 a112a111a117a122a101 a110a97 a116a111a109a44
a107a116a101a114a233 a107a97a114a116a121 a104a114a225a163 a100a111a115a116a97a108a46a41
a144a101a178a101a110a237a58 a75a100a121a98a121 a110a97 a112a111a176a97a100a237 a107a97a114a101a116 a122a225a108a101a186a101a108a111a44 a98a121a108a105 a98a121a99a104a111a109 a118a101 a115a116a101a106a110a233 a115a105a116a117a97a99a105 a106a97a107a111 a118 a112a176a237a107a108a97a100a117 a49a46a53a46
a146a108a111 a98a121 a111 a118a97a114a105a97a99a101 a98a101a122 a111a112a97a107a111a118a225a110a237a46 a80a114a118a110a237 a107a97a114a116a97 a98a121 a109a111a104a108a97 a98a253a116 a107a116a101a114a225a107a111a108a105 a122 a51a50a44 a107 a110a237 a100a114a117a104a225 a112a97a107
a107a116a101a114a225a107a111a108a105 a122 a51a49a44 a97a116a100a46 a67a101a108a107a101a109 a98a121a99a104a111a109 a109a165a108a105 32·31·30·29·28 = 24165120 a109a111a186a110a111a115a116a237a46 a74a101a110a186a101 a122a100a101
a110a97 a112a111a176a97a100a237 a107a97a114a101a116 a110a101a122a225a108a101a186a237a46 a85a115a112a111a176a225a100a97a110a225 a112a165a116a105a99a101 K♥,Q♣,10♥,8♦,7♠ a104a114a225a163a105 a118a121a106a100a101 a110a97a115a116a101a106a110a111
a106a97a107a111 8♦,Q♣,7♠,K♥,10♥a46 a86a178a101a99a104 24165120 a109a111a186a110a111a115a116a237 a112a114a111a116a111 a109a183a186a101a109a101 a114a111a122a100a165a108a105a116 a100a111 a40a111a112a165a116
a122a97a116a237a109 a110a101a122a110a225a109a233a104a111 a112a111a163a116a117a41 a115a107a117a112a105a110a46 a75a97a186a100a225 a115a107a117a112a105a110a97 a115a101 a115a107a108a225a100a225 a122 a112a165a116a105a99 a107a97a114a101a116a44 a107a116a101a114a233 a115a101 a108a105a178a237 a112a111a117a122a101
a112a111a176a97a100a237a109a46 a80a165a116 a107a97a114a101a116 a109a183a186a101a109a101 a112a176a101a115a107a117a112a105a116 5! a122a112a183a115a111a98a121a44 a107a97a186a100a225 a115a107a117a112a105a110a97 a109a225 a112a114a111a116a111 5! a112a114a118a107a183a46 a80a111a163a101a116
a115a107a117a112a105a110 a110a101a98a111a108a105 a112a111a163a101a116 a118a178a101a99a104 a114a183a122a110a253a99a104 a112a165a116a105a99 a107a97a114a101a116 a115a101a115a116a97a118a105a116a101a108a110a253a99a104 a122 a51a50 a107a97a114a101a116 a106a101 a112a114a111a116a111
32·31·30·29·28
5! .
a83 a116a237a109a116a111 a118a253a115a108a101a100a107a101a109 a109a183a186a101a109a101 a106a101a178a116a165 a99a104a118a237a108a105 a18a163a97a114a111a118a97a116a16a46 a90a108a111a109a101a107 a114a111a122a178a237a176a237a109a101 a118a253a114a97a122a101a109 27!a46 a80a111 a250a112a114a97a118a165
a112a97a107 a100a111a115a116a97a110a101a109a101 a118a253a115a108a101a100a101a107 a118 a107a111a109a112a97a107a116a110a165a106a178a237a109 a116a118a97a114a117a58
32·31·30·29·28
5! =
32·31·30·29·28·27!
5!·27! =
32!
5!·27!
a74a105a110a253 a122a112a183a115a111a98 a176a101a178a101a110a237a58 a80a176a101a100a115a116a97a118a109a101 a115a105a44 a186a101 a109a225a109a101 a107a97a114a116a121 a110a165a106a97a107 a117a115a112a111a176a225a100a97a110a233a44 a110a97a112a176a46
A♥,A♦,A♠,A♣,K♥,K♦,...,7♥,7♦,7♠,7♣a46 a75a97a186a100a225 a112a165a116a105a99a101 a107a97a114a101a116 a115a101 a116a101a164 a100a225 a105a110a116a101a114a112a114a101a116a111a45
a118a97a116 a106a97a107a111 a51a50a45a163a108a101a110a110a225 a112a111a115a108a111a117a112a110a111a115a116 a112a165a116a105 a106a101a100a110a105a163a101a107 a97 a100a118a97a99a101a116a105 a115a101a100a109a105 a110a117a108a46 a74a101a100a110a105a163a107a121 a106a115a111a117 a110a97 a109a237a115a116a101a99a104
a118a121a98a114a97a110a253a99a104 a107a97a114a101a116a44 a110a117a108a121 a110a97 a118a178a101a99a104 a111a115a116a97a116a110a237a99a104a46 a78a97a112a176a46 a112a111a115a108a111a117a112a110a111a115a116 (1,0,1,0,0,1,0,...,0,1,1)
a98a121 a122a110a97a109a101a110a97a108a97a44 a186a101 a104a114a225a163 a100a111a115a116a97a108 A♥,A♠,K♦,7♠ a97 7♣a46 a90a97a100a97a110a111a117 a111a116a225a122a107a117 a116a101a164 a109a183a186a101a109a101 a112a176a101a118a233a115a116
a110a97 a112a114a111a98a108a233a109a44 a107a111a108a105a107a97 a122a112a183a115a111a98a121 a108a122a101 a110a97a118a122a225a106a101a109 a112a176a101a115a107a117a112a105a116 a112a165a116 a106a101a100a110a105a163a101a107 a97 a50a55 a110a117a108a46 a78a97 a116a117a116a111 a111a116a225a122a107a117
a117a186 a97a108a101 a111a100a112a111a118a165a164 a122a110a225a109a101a46 a74a100a101 a111 a110a165a99a111 a112a111a100a111a98a110a233a104a111 a106a97a107a111 a118 a112a176a237a107a108a97a100a117 a115 a97a110a97a110a97a115a101a109 a97 a118a253a115a108a101a100a101a107 a106a101
32!
5!·27! .
a79a98a165a109a97 a122a112a183a115a111a98a121 a106a115a109a101 a100a111a115a112a165a108a105 a107 a116a233a109a117a186 a118a253a115a108a101a100a107a117a44 a107a116a101a114a253 a112a111 a118a121a163a237a115a108a101a110a237 a100a225 201376 a109a111a186a110a253a99a104 a112a165a116a105a99
a115a101a115a116a97a118a105a116a101a108a110a253a99a104 a122 a51a50 a107a97a114a101a116a46
a56 a70a97a107a117a108a116a97 a101a108a101a107a116a114a111a116a101a99a104a110a105a107a121 a97 a107a111a109a117a110a105a107a97a163a110a237a99a104 a116a101a99a104a110a111a108a111a103a105a237 a86a85a84 a118 a66a114a110a165
a84a101a110a116a111 a112a176a237a107a108a97a100 a98a121a108 a118a101a108a109a105 a100a183a108a101a186a105a116a253a46 a79a116a225a122a107a97a44 a107a111a108a105a107a97 a122a112a183a115a111a98a121 a108a122a101 a118a121a98a114a97a116 a122 na45a112a114a118a107a111a118a233 a109a110a111a186a105a110a121 ka45
a112a114a118a107a111a118a111a117 a115a107a117a112a105a110a117a44 a118a101 a107a116a101a114a233 a110a101a122a225a108a101a186a237 a110a97 a112a111a176a97a100a237a44 a97a108a101 a112a111a117a122a101 a110a97 a116a111a109a44 a107a116a101a114a233 a112a114a118a107a121 a98a121a108a121 a118a121a98a114a225a110a121a44
a115a101 a118a121a115a107a121a116a117a106a101 a118a101a108a109a105 a163a97a115a116a111a46 a86 a112a114a225a118a165 a112a176a101a100a118a101a100a101a110a233a109 a112a176a237a107a108a97a100a117 a106a115a109a101 a111a100a118a111a100a105a108a105 a118a122a116a97a104 a112a114a111 a118a253a112a111a163a101a116
a112a111a163a116a117 a112a165a116a105a112a114a118a107a111a118a253a99a104 a112a111a100a109a110a111a186a105a110 a122 a100a118a97a97a116a176a105a99a101a116a105a112a114a118a107a111a118a233 a109a110a111a186a105a110a121a46 a86 a110a225a115a108a101a100a117a106a237a99a237a109 a114a225a109a101a163a107a117
a106a101 a115a105a116a117a97a99a101 a112a111a112a115a225a110a97 a111a98a101a99a110a165a46
a75a111a109a98a105a110a97a99a101a44 a107a111a109a98a105a110a97a163a110a237 a163a237a115a108a97
a75a111a109a98a105a110a97a99a101 ka45a116a233 a116a176a237a100a121 a122 n a112a114a118a107a183 a106a115a111a117 ka45a112a114a118a107a111a118a233 a115a107a117a112a105a110a121 a118a121a98a237a114a97a110a233 a122 na45a112a114a118a107a111a118a233 a109a110a111a186a105a110a121a44
a112a176a105a163a101a109a186 a110a101a122a225a108a101a186a237 a110a97 a112a111a176a97a100a237a44 a118 a106a97a107a233a109 a112a114a118a107a121 a98a121a108a121 a118a121a98a114a225a110a121a46
a74a105a110a253a109a105 a115a108a111a118a121a44 a106a115a111a117 a116a111 ka45a112a114a118a107a111a118a233 a112a111a100a109a110a111a186a105a110a121 a122 a109a110a111a186a105a110a121 a109a97a106a237a99a237 n a112a114a118a107a183a46
a80a111a163a101a116 a116a97a107a111a118a253a99a104a116a111 a107a111a109a98a105a110a97a99a237 a106a101
parenleftbign
k
parenrightbig= n!
k!·(n−k)! .
a83a121a109a98a111a108 parenleftbignkparenrightbig a163a116a101a109a101 a18n a110a97a100 ka16 a97 a110a97a122a253a118a225a109a101 a106a101a106 a107a111a109a98a105a110a97a163a110a237 a163a237a115a108a111a46
a85 a107a97a114a101a116 a106a101a178a116a165 a99a104a118a237a108a105 a122a183a115a116a97a110a101a109a101 a97 a122a107a117a115a237a109a101 a111 a110a165a99a111 a115a108a111a186a105a116a165a106a178a237 a112a176a237a107a108a97a100a121a46 a86a253a112a111a163a116a121 a107a111a109a98a105a110a97a163a110a237a99a104
a163a237a115a101a108 a112a114a111 a106a105a115a116a111a116a117 a118 a112a114a118a110a237a99a104 a110a165a107a111a108a105a107a97 a112a176a237a112a97a100a101a99a104 a114a111a122a101a112a237a178a101a109a101a46
a80a176a237a107a108a97a100 a49a46a49a48 a75a111a108a105a107a97 a122a112a183a115a111a98a121 a109a183a186a101a109a101 a122 a98a97a108a237a163a107a117 a53a50 a107a97a114a101a116 a404×13 a107a97a114a101a116 a118 a98a97a114a118a225a99a104 ♥,♦,♠,♣
a111 a104a111a100a110a111a116a225a99a104 a50a44 a51a44 a46a46a46a44 a75a44 a65a41 a118a121a98a114a97a116 a112a165a116a105a99a105 a107a97a114a101a116a44 a118 a107a116a101a114a233 a106a115a111a117 a112a114a225a118a165 a100a118a165 a101a115a97a63
a144a101a178a101a110a237a58 a78a101a106a112a114a118a101 a115a101 a112a111a100a237a118a225a109a101a44 a107a111a108a105a107a97 a122a112a183a115a111a98a121 a108a122a101 a122 a98a97a108a237a163a107a117 a118a121a98a114a97a116 a100a118a111a106a105a99a105 a101a115a46 a69a115a97 a109a225a109a101
a99a101a108a107a101a109 a52a44 a122 a110a105a99a104 a118a121a98a237a114a225a109a101 a100a118a111a106a105a99a105a44 a110a101a122a225a108a101a186a237 a110a225a109 a110a97 a116a111a109a44 a118 a106a97a107a233a109 a112a111a176a97a100a237 a106a115a109a101 a107a97a114a116a121 a118a121a98a114a97a108a105a44
a97a108a101 a106a101a110 a110a97 a116a111a109a44 a122 a107a116a101a114a253a99a104 a101a115 a115a101 a100a118a111a106a105a99a101 a115a107a108a225a100a225a46 a80a111a163a101a116 a118a178a101a99a104 a109a111a186a110a253a99a104 a100a118a111a106a105a99 a106a101 a112a114a111a116a111
parenleftbigg4
2
parenrightbigg
= 4!2!·2! = 4·3·2·12·1·2·1 = 6.
a74a101a115a116a108a105a186a101 a117a186 a106a101 a110a165a106a97a107a225 a100a118a111a106a105a99a101 a101a115 a118a121a98a114a225a110a97a44 a109a117a115a237a109a101 a107 a110a237 a21 a112a114a111 a100a111a112a108a110a165a110a237 a100a111 a112a165a116a105a99a101 a21 a118a121a98a114a97a116
a106a101a178a116a165 a116a176a105 a107a97a114a116a121 a106a105a110a233 a110a101a186 a101a115a97a46 a84a97a107a111a118a253a99a104a116a111 a107a97a114a101a116 a109a225a109a101 a52a56a44 a118a121a98a237a114a225a109a101 a122 a110a105a99a104 a116a114a111a106a105a99a105a46 a80a114a111 a116a101a110a116a111
a118a253a98a165a114 a106a101 a112a111a163a101a116 a109a111a186a110a111a115a116a237
parenleftbigg48
3
parenrightbigg
= 48!3!·45! = 48·47·46·45!3·2·1·45! = 17296.
a78a121a110a237 a112a111a117a186a105a106a101a109a101 a112a114a97a118a105a100a108a111 a115a111a117a163a105a110a117 a21 a100a118a111a106a105a99a105 a101a115 a108a122a101 a118a121a98a114a97a116 parenleftbig42parenrightbig a122a112a183a115a111a98a121a44 a107a101 a107a97a186a100a233 a116a97a107a111a118a233a116a111
a100a118a111a106a105a99a105 a108a122a101 a122a98a253a118a97a106a237a99a237 a116a114a111a106a105a99a105 a100a111a112a108a110a105a116 parenleftbig483parenrightbig a122a112a183a115a111a98a121a44 a112a165a116a105a99a105 a115a108a111a186a101a110a111a117 a122a101 a100a118a111a117 a101a115 a97 a116a176a237 a18a110a101a45a101a115a16
a109a183a186a101a109a101 a112a114a111a116a111 a115a101a115a116a97a118a105a116
parenleftbigg4
2
parenrightbigg
·
parenleftbigg48
3
parenrightbigg
= 6·17296 = 103776
a122a112a183a115a111a98a121a46
a75a111a109a98a105a110a97a163a110a237 a163a237a115a108a97 a115a101 a100a97a106a237 a115a110a97a100a110a111 a118a121a112a111a163a237a116a97a116 a112a111a109a111a99a237 a116a122a118a46 a80a97a115a99a97a108a111a118a97 a116a114a111a106a250a104a101a108a110a237a107a97a46 a84a237a109a116a111
a110a225a122a118a101a109 a111a122a110a97a163a117a106a101a109a101 a116a97a98a117a108a107a117 a116a114a111a106a250a104a101a108a110a237a107a111a118a233a104a111 a116a118a97a114a117
a77a97a116a101a109a97a116a105a107a97 a51 a57
n = 0 a49
n = 1 a49 a49
n = 2 a49 a50 a49
n = 3 a49 a51 a51 a49
n = 4 a49 a52 a54 a52 a49
n = 5 a49 a53 a49a48 a49a48 a53 a49
n = 6 a49 a54 a49a53 a50a48 a49a53 a54 a49
a75a97a186a100a253 a176a225a100a101a107 a122a100a101 a111a98a115a97a104a117a106a101 a118a178a101a99a104a110a97 a107a111a109a98a105a110a97a163a110a237 a163a237a115a108a97 a112a114a111 a116a111a116a233a186 n. a80a111a100a108a101 a122a110a225a109a233a104a111 a118a122a111a114a99a101a44parenleftbig
n
k
parenrightbig+parenleftbig n
k+1
parenrightbig = parenleftbign+1
k+1
parenrightbig, a100a111a115a116a97a110a101a109a101 a115a101a163a116a101a110a237a109 a100a118a111a117 a115a111a117a115a101a100a110a237a99a104 a107a111a109a98a105a110a97a163a110a237a99a104 a163a237a115a101a108 a110a165a107a116a101a114a233a104a111
a176a225a100a107a117 a116a111 a107a111a109a98a105a110a97a163a110a237 a163a237a115a108a111a44 a106a101a186 a115a116a111a106a237 a118 a100a97a108a178a237a109 a176a225a100a107a117 a112a111a100 a109a101a122a101a114a111a117 a109a101a122a105 a110a105a109a105a46 a80a97a115a99a97a108a183a118
a116a114a111a106a250a104a101a108a110a237a107 a116a97a107 a109a183a186a101 a115a108a111a117a186a105a116 a107 a100a111a115a116a105 a114a121a99a104a108a233a109a117 a118a253a112a111a163a116a117 a107a111a109a98a105a110a97a163a110a237a99a104 a163a237a115a101a108a46
a80a176a237a107a108a97a100 a49a46a49a49 a75a111a108a105a107a97 a122a112a183a115a111a98a121 a109a183a186a101a109a101 a122 a98a97a108a237a163a107a117 a53a50 a107a97a114a101a116 a118a121a98a114a97a116 a54 a107a97a114a101a116 a116a97a107a44 a97a98a121 a110a97a110a101a106a118a253a178
a106a101a100a110a97 a122 a118a121a98a114a97a110a253a99a104 a107a97a114a101a116 a98a121a108a97 a112a105a107a111a118a225a63
a144a101a178a101a110a237a58 a77a225a45a108a105 a98a253a116 a118a101 a118a121a98a114a97a110a233 a178a101a115a116a105a99a105 a110a97a110a101a106a118a253a178 a106a101a100a110a97 a112a105a107a111a118a225 a107a97a114a116a97a44 a122a110a97a109a101a110a225 a116a111a44 a186a101 a178a101a115a116a105a99a101
a111a98a115a97a104a117a106a101 a98a117a164 a112a114a225a118a165 a106a101a100a110a117 a116a97a107a111a118a111a117 a107a97a114a116a117a44 a110a101a98a111 a186a225a100a110a111a117a46 a67a101a108a107a111a118a253 a112a111a163a101a116 a112a114a111a116a111 a100a111a115a116a97a110a101a109a101 a116a97a107a44
a186a101 a115a101a163a116a101a109a101 a112a111a163a101a116 a178a101a115a116a105a99 a115a107a108a225a100a97a106a237a99a237a99a104 a115a101 a122 a106a101a100a110a233 a112a105a107a111a118a233 a107a97a114a116a121 a40a116a97a107a111a118a253a99a104a116a111 a107a97a114a101a116 a109a225a109a101 a99a101a108a107a101a109
a107 a100a105a115a112a111a122a105a99a105 a49a51a41 a97 a112a165a116a105 a106a105a110a253a99a104 a107a97a114a101a116 a40a106a105a110a253a99a104 a107a97a114a101a116 a106a101 a99a101a108a107a101a109 a51a57a41 a97 a112a111a163a101a116 a178a101a115a116a105a99 a115a108a111a186a101a110a253a99a104
a122a101 a115a97a109a253a99a104 a107a97a114a101a116 a106a105a110a253a99a104 a110a101a186 a112a105a107a111a118a253a99a104a46 a74a101a100a110a111a116a108a105a118a233 a112a111a163a116a121 a117a114a163a237a109a101 a112a111a100a111a98a110a165 a106a97a107a111 a118 a112a176a101a100a99a104a111a122a237a109
a112a176a237a107a108a97a100a117a44 a99a101a108a107a111a118a253 a118a253a115a108a101a100a101a107 a106a101 a112a97a107
13·
parenleftbigg39
5
parenrightbigg
+
parenleftbigg39
6
parenrightbigg
.
a80a111a115a116a117a112 a112a111a117a186a105a116a253 a118 a116a111a109a116a111 a112a176a237a107a108a97a100a117 a109a183a186a101a109a101 a122a111a98a101a99a110a105a116a46 a131a97a115a116a111 a115a101 a112a111a100a97a176a237 a111a98a106a101a107a116a121a44 a106a101a106a105a99a104a186 a112a111a163a101a116
a99a104a99a101a109a101 a122a106a105a115a116a105a116a44 a114a111a122a100a165a108a105a116 a100a111 a118a237a99a101 a115a107a117a112a105a110a44 a106a101a106a105a99a104a186 a112a111a163a116a121 a112a114a118a107a183 a117a109a237a109a101 a117a114a163a105a116a46 a67a101a108a107a111a118a253 a112a111a163a101a116
a111a98a106a101a107a116a183 a106a101 a112a97a107 a114a111a118a101a110 a115a111a117a163a116a117 a112a111a163a116a183 a112a114a118a107a183 a106a101a100a110a111a116a108a105a118a253a99a104 a115a107a117a112a105a110a46 a77a117a115a237a109a101 a118a178a97a107 a100a225a116 a112a111a122a111a114 a110a97
a116a111a44 a97a98a121 a106a101a100a110a111a116a108a105a118a233 a115a107a117a112a105a110a121 a98a121a108a121 a100a105a115a106a117a110a107a116a110a237a44 a116a106a46 a97a98a121 a186a225a100a110a253 a111a98a106a101a107a116 a110a101a115a112a97a100a97a108 a100a111 a118a237a99a101 a115a107a117a112a105a110
a115a111a117a163a97a115a110a165a46 a74a97a107a111 a118a97a114a111a118a225a110a237 a98a121 a110a225a109 a109a111a104a108 a112a111a115a108a111a117a186a105a116 a110a225a115a108a101a100a117a106a237a99a237 a112a176a237a107a108a97a100a46
a80a176a237a107a108a97a100 a49a46a49a50 a74a105a115a116a225 a118a121a115a111a107a225 a178a107a111a108a97 a112a114a111a109a237a106a237 a112a176a105a106a237a109a97a99a237 a122a107a111a117a178a107a117 a117a99a104a97a122a101a163a183a109a44 a107a116a101a176a237 a109a97a116a117a114a111a118a97a108a105
a122 a109a97a116a101a109a97a116a105a107a121 a110a101a98a111 a122 a102a121a122a105a107a121 a97 a100a111a115a225a104a108a105 a97a108a101a115a112a111a172 a122 a106a101a100a110a111a104a111 a122 a116a165a99a104a116a111 a112a176a101a100a109a165a116a183 a107a108a97a115a105a28a107a97a99a101
a118a253a98a111a114a110a165a46 a90 a99a101a108a107a111a118a233a104a111 a112a111a163a116a117 a49a48a48a48 a112a176a105a104a108a225a178a101a110a253a99a104 a110a97 a116a117a116a111 a178a107a111a108a117 a109a97a116a117a114a111a118a97a108a111 a122 a109a97a116a101a109a97a116a105a107a121 a110a97
a118a253a98a111a114a110a111a117 a49a48a48 a117a99a104a97a122a101a163a183 a97 a122 a102a121a122a105a107a121 a56a48a46 a75a111a108a105a107 a117a99a104a97a122a101a163a183 a98a117a100a101 a112a176a105a106a97a116a111 a98a101a122 a112a176a105a106a237a109a97a99a237 a122a107a111a117a178a107a121a63
a80a111a107a117a115 a111 a176a101a178a101a110a237a58 a78a165a107a100a111 a98a121 a115a105 a116a176a101a98a97 a109a111a104a108 a176a237a99a116a44 a186a101 a118a253a115a108a101a100a101a107 a106a101
100 + 80 = 180.
a84a101a110a116a111 a118a253a115a108a101a100a101a107 a118a178a97a107 a118a183a98a101a99 a110a101a109a117a115a237 a98a253a116 a115a112a114a225a118a110a253a46 a85a99a104a97a122a101a163a105a44 a107a116a101a176a237 a109a97a116a117a114a111a118a97a108a105 a122a97 a106a101a100a110a97
a122 a109a97a116a101a109a97a116a105a107a121 a105 a122 a102a121a122a105a107a121a44 a106a115a111a117 a122a100a101 a122a97a112a111a163a237a116a225a110a105 a100a118a97a107a114a225a116a46 a78a97 a122a225a107a108a97a100a165 a105a110a102a111a114a109a97a99a237a44 a107a116a101a114a233 a109a225a109a101a44
a110a101a106a115a109a101 a115a99a104a111a112a110a105 a112a111a163a101a116 a108a105a100a237 a112a176a105a106a97a116a253a99a104 a98a101a122 a112a176a105a106a237a109a97a163a101a107 a112a176a101a115a110a165 a117a114a163a105a116a46 a75a100a121a98a121a99a104a111a109 a97a108a101 a110a97a118a237a99
a118a165a100a165a108a105a44 a186a101 a51a48 a117a99a104a97a122a101a163a183 a109a97a116a117a114a111a118a97a108a111 a110a97 a118a253a98a111a114a110a111a117 a122 a111a98a111a117 a112a176a101a100a109a165a116a183a44 a250a108a111a104a97 a98a121 a106a105a186 a176a101a178a105a116a101a108a110a225
a98a121a108a97a46 a80a111a163a101a116 a112a176a105a106a97a116a253a99a104 a98a101a122 a112a176a105a106a237a109a97a99a237 a122a107a111a117a178a107a121 a98a121 a98a121a108
100 + 80−30 = 150.
a49a48 a70a97a107a117a108a116a97 a101a108a101a107a116a114a111a116a101a99a104a110a105a107a121 a97 a107a111a109a117a110a105a107a97a163a110a237a99a104 a116a101a99a104a110a111a108a111a103a105a237 a86a85a84 a118 a66a114a110a165
a86a122a97a108a105 a106a115a109a101 a49a48a48 a108a105a100a237a44 a107a116a101a176a237 a109a97a106a237 a106a101a100a110a105a163a107a117 a122 a109a97a116a101a109a97a116a105a107a121a44 a97 a107 a110a105a109 a106a115a109a101 a112a176a105a100a97a108a105 a122 a116a165a99a104a44 a107a100a111
a109a97a106a237 a106a101a100a110a105a163a107a117 a122 a102a121a122a105a107a121a44 a106a101a110 a116a121a44 a107a116a101a176a237 a106a101a178a116a165 a110a101a98a121a108a105 a122a97a112a111a163a237a116a225a110a105 a118 a18a109a97a116a101a109a97a116a105a99a237a99a104a16a46
a79a98a101a99a110a165 a106a101 a176a101a178a101a110a237 a110a97a178a101a104a111 a112a176a237a107a108a97a100a117
100 + 80−m, a107a100a101 m a106a101 a112a111a163a101a116 a117a99a104a97a122a101a163a183 a115 a106a101a100a110a105a163a107a111a117 a122 a111a98a111a117 a112a176a101a100a109a165a116a183a46
a80a176a237a107a108a97a100 a49a46a49a51 a75a111a108a105a107 a108a122a101 a115a101a115a116a97a118a105a116 a112a165a116a105a99a105a102a101a114a110a253a99a104 a163a237a115a101a108 a122 a163a237a115a108a105a99 1,2,3a44 a116a97a107a111a118a253a99a104 a186a101 a110a97 a122a97a163a225a116a107a117
a110a101a98a111 a110a97 a107a111a110a99a105 a106a101 a106a101a100a110a105a163a107a97a63
a144a101a178a101a110a237a58 a131a237a115a101a108a44 a107a116a101a114a225 a122a97a163a237a110a97a106a237 a106a101a100a110a105a163a107a111a117a44 a106a101 34 a40a110a97 a112a114a118a110a237a109 a109a237a115a116a165 a106a101 a110a97a112a101a118a110a111 a106a101a100a110a105a163a107a97a44 a110a97
a100a114a117a104a233a109 a97a186 a112a225a116a233a109 a109a237a115a116a165 a109a18