Tasty Chicken Nuggets
McDonald's sells packets of Chicken Nuggets in three different packet types.
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Packet Mini - 6 Nuggets
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Packet Single - 9 Nuggets.
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Packet Family - 20 Nuggets.
What is the maximum number of nuggets that cannot be ordered from the outlet?
Image Credit: Wikimedia McDonald's
The answer is 43.
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1 solution
We shall first study numbers from 1 to 100. Except 3, any number divisible by 3 can be packed with combination of 6 and 9.
S o 4 ∗ 6 + 2 0 = 4 4 , . . . . . . . 5 ∗ 9 = 4 5 , . . . . . . . 2 ∗ 2 0 + 6 = 4 6 . 4 4 ≡ 2 ( m o d 3 ) . . . . . . . . . 4 5 ≡ 0 ( m o d 3 ) , . . . . . . . . . . 4 6 ≡ 1 ( m o d 3 ) . A n d w e c a n a d d 3 a n d i t s m u l t i p l e t o r e a c h 1 0 0 , a n d 5 ∗ 2 0 t o a n y n u m b e r o f h u n d r e d s . ⟹ a l l n u m b e r s 4 4 a n d g r e a t e r c a n b e p a c k e d . T h e r e i s n o w a y t o p a c k 4 3 .