You don't need to say a thing Part 2

Logic Level 1

I am thinking of 3 numbers such that their mean, mode, and median are all equal to 11. What is the product of these numbers?

The answer is 1331.

6 solutions

Brock Brown
Jul 18, 2015

If we know the mode is $11$ , we know at least two of the numbers must be $11$ . So our tuple becomes the following: $(x, 11, 11)$ .

If we know the mean is 11, then...

$\frac{x + 11 + 11}{3} = 11 \implies x + 22 = 33 \implies x = 11$

We now know our tuple is $(11, 11, 11)$ ; this also satisfies the condition $median = 11$ .

This implies the answer is $11 \times 11 \times 11 = \boxed{1331}$ .

Without clarifying that its a single mode set, its really not conclusive.

8-11-14 is a solution with 11 as a mode of the set (just not the only mode)

Scott Dobson - 5 years, 10 months ago

He clarifies it's a single mode set when he says that $mode = 11$ ; if he said $11 \in mode$ , you'd be right, but he says equals . Your $(8, 11, 14)$ solution can't be true because $mode = 11 \neq 14 \neq 8$ .

Brock Brown - 5 years, 10 months ago

what is a tuple?

Nelson Mandela - 5 years, 11 months ago

A tuple is a finite list of elements; in this case, it's a list of numbers.

Brock Brown - 5 years, 11 months ago

Tuples are ordered.

Venkata Karthik Bandaru - 5 years, 11 months ago

CHALLENGE MASTER NOTE: Too hard to understand. Python is preferred.

Pi Han Goh - 5 years, 11 months ago

You're absolutely right. What was I thinking?

Python 3.3:

from functools import reduce
def mean(numbers):
    return sum(numbers)/len(numbers)
def median(numbers):
    return numbers[int((len(numbers) - 1)/2)]
def mode(numbers):
    count = {}
    for number in numbers:
        if number not in count:
            count[number] = 0
        count[number] += 1
    best = None
    highest = 1
    for number in count:
        if count[number] > highest:
            best = number
            highest = count[number]
        elif count[number] == highest:
            best = None
    return best
def goal(numbers):
    return mean(numbers) == 11 and\
        median(numbers) == 11 and\
        mode(numbers) == 11
def product(numbers):
    return reduce(lambda a,b:a*b, numbers)
solved = False
a = 0
while not solved:
    b = 0
    while b <= a and not solved:
        c = 0
        while c <= b and not solved:
            if goal((a, b, c)):
                solved = True
                print ("Answer:", product((a, b, c)))
            c += 1
        b += 1
    a += 1

Brock Brown - 5 years, 10 months ago

Ah, now that looks so much clearer. Thanks for elucidating your solution.

Pi Han Goh - 5 years, 10 months ago

Lol XD ! Brock, I want a python solution for this !

Venkata Karthik Bandaru - 5 years, 10 months ago

Vijay K
Aug 9, 2015

mean= just like average mode= max no of terms repeated in the sequence median= middle term of the sequence

Sadasiva Panicker
Aug 8, 2015

Not mentioned the three numbers are different. So the three numbers are 11,11 and 11. Then Mean = 11; Median = 11 And Mode = 11. There fore Product of the three numbers + 11 x 11 x 11 =1331.

Moderator note:

Yes it works for 11,11,11. But how do you know that they are the only numbers that satisfy this condition?

Refer to Brock's solution for the proper approach.

I agree with Sadasiva Panicker. The question necessarily assumes that there is either only one set of three numbers that produces a solution, or that the product is the same for all solutions. So finding the product from any solution that works is an adequate method to get this right. My reasoning was - this would work if all the numbers were 11, so I'm going to submit (11 x 11 x 11=) 1331 as the answer.

Peter Reynolds - 5 years, 10 months ago

Devasish Basu
Aug 9, 2015

Median is the central number which is 11 then. Mode is the highest frequency. Since 11 is already a number, so, its occurrence has to be more than other numbers to be the mode. So there are more than one 11's which makes the mean different from 11 if the third number is not 11. Therefore, all the three numbers are 11.

Hadia Qadir
Aug 12, 2015

The product is 11^3 = 1331.

Andriane Casuga
Aug 10, 2015

The product is 11^3 = 1331. Please consider

You don't need to say a thing Part 2

The answer is 1331.

6 solutions

Moderator note:

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