Question of the test of the Brazilian naval college

Question

Determine the number of digits required for the even numbers from 6 to 281 inclusive a) 356 b)830 c)546 d)637 e)365

I'm improving my English yet ...

This might be a trick question. The number of digits required seems to be ten: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$. All the numbers from $6$ to $281$ can be formed out of those digits. — Mark Fischler, Apr 26 '19 at 21:16
I tried to use arithmetic progression but did not hit with the alternatives — Lambert macuse, Apr 26 '19 at 21:31

score 1 · Answer 1 · answered Apr 26 '19 at 21:20

1

If this is not a trick question, it is easy. There are $4$ single digit numbers $(6,7,8,9)$. There are $90$ two-digit numbers $(10, 11, \ldots , 99)$. There are $182$ three-digit numbers. Note that the easy way to count is to consider "half-open" ranges of the form "at least $a$ but smaller than $b$." Thus $282 - 100 = 182$. And $10 - 6 = 4$.

The answer is $$1\cdot 4 + 90 \cdot 2 + 182 \cdot 3$$

answered Apr 26 '19 at 21:20

Mark Fischler

41,743

1

Did you miss $\bf{even}$? – Apr 26 '19 at 21:32

score 0 · Accepted Answer · answered Apr 26 '19 at 22:23

Good luck on your Naval Academy Exams!

So verbal language might be less effective in helping you visualize the problem. I will try to convey this with a little bit of python. If of course my assumptions about the problem are valid.

numbers = range(6,282)
even_numbers = []
for i in numbers:
    if i%2!=1:
        even_numbers.append(i)

#print(even_numbers)
#print(len(even_numbers))        

single_digits = []
double_digits = []
triple_digits = []

for i in even_numbers:
    if i<10:
        single_digits.append(i)
    if i in range(10,99):
        double_digits.append(i)
    if i in range(99,282):
        triple_digits.append(i)


print(single_digits)
print(double_digits)
print(triple_digits)

print(len(single_digits)+len(double_digits)*2+len(triple_digits)*3)

Outputs to the console:

[6, 8] [10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98] [100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 254, 256, 258, 260, 262, 264, 266, 268, 270, 272, 274, 276, 278, 280] 365

365

What I have done is simply make a list of all numbers from 6-281 for you with a little code and have selected the even numbers and put them into lists based on digit value for you to see.

Mark Fischler is absolutely correct and with a bit more sensitivity towards numbers we might have been fast to realize his answer is correct, and all you had to do was divide it by 2 to get the even or odd values.

I am sure that I could be misinterpreting your question as the word "digits" is some what confusing here... I hope this helps.

TL;DR

Fantastic answer Mark Fischler, Follow his words! The correct answer is 365.

Thank you!
Make sure to study how Mark Fischler solved the problem without code and then just ask yourself if the question is asking odd, even, or both? if both do nothing, if odd or even than divide your answer.

This was a very fun question. Maybe practice a few by changing the number range from 6-282 to 1203-1182 or something to quiz yourself. Good day, you got this! — jbussing, Apr 26 '19 at 23:10

Question of the test of the Brazilian naval college

2 Answers2