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Difficulty:
95%
(hard)
Question Stats:
33% (02:22) correct
67%
(02:26)
wrong
based on 45
sessions
History
Date
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Not Attempted Yet
A pizzería rightly claims that a customer could order a different pizza every day of the year from the available toppings, without repeating a pizza ordered earlier in the year or changing the number of toppings ordered. If the list of available toppings never changes, what is the smallest possible number of toppings on the list? (Two pizzas are considered different if and only if they do not have the same toppings)
A. 9
B. 10
C. 11
D. 27
E. 28
A. 9
B. 10
C. 11
D. 27
E. 28
28 Aug 2026, 11:43
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We need the smallest number of available toppings such that the customer can make at least 365 different pizzas, while ordering the same number of toppings each day.
Suppose there are n toppings, and the customer orders exactly k toppings each time.
The number of different pizzas is: C(n,k)
We need: C(n,k) >= 365
To get the most combinations for a given n, choose k close to n/2.
Try n = 10:
C(10,5) = 252 < 365
So 10 toppings are not enough.
Try n = 11:
C(11,5) = 462 > 365
Therefore, the smallest possible number of toppings is: 11.
Suppose there are n toppings, and the customer orders exactly k toppings each time.
The number of different pizzas is: C(n,k)
We need: C(n,k) >= 365
To get the most combinations for a given n, choose k close to n/2.
Try n = 10:
C(10,5) = 252 < 365
So 10 toppings are not enough.
Try n = 11:
C(11,5) = 462 > 365
Therefore, the smallest possible number of toppings is: 11.
28 Aug 2026, 14:15
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Hi can you explain why did you half the topping in both the cases and the question says diff toppings right ?
Can you please explain this
Is there any other way to solve this ?
Can you please explain this
Is there any other way to solve this ?
paragw
29 Aug 2026, 09:42
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For any given number of toppings available , if you want to maximize the number of distinct pizzas you can order with a set number of toppings, the number of toppings you choose should be half of the number of toppings available (in the case the number of toppings available is even) or half of 1 less than the number of toppings available (in the case that the number of toppings is odd)
