TotallyOriginallyCreatedByMe Number

Computer Science Level 4

Let $\overline{a_1 a_2 a_3 \ldots a_n}$ be the smallest $n$ -digit number greater than $1$ with $a_1, a_2, a_3, \ldots, a_n \ne 0$ such that $\large \displaystyle \sum_{k=1}^n a_k^{a_k} = \overline{a_1 a_2 a_3 \ldots a_n}$ . What is the value of $\displaystyle \prod_{k=1}^n a_k$ ?

The answer is 180.

3 solutions

Thaddeus Abiy
May 10, 2014

The original python script I wrote:

n = 1
while True:
    n +=1
    if sum([pow(int(x),int(x)) for x in str(n)])==n:
        print n
        break

An expanded version for readability purposes:

n = 1
while True:
    n += 1
    Sum = 0
    for an in str(n):
        Sum += pow(int(an),int(an))
    if Sum == n:
        print n
        break

Canouchi number / Münchhausen Number

Pi Han Goh - 7 years, 1 month ago

lol "TotallyOriginallyCreatedbyMe"

Thaddeus Abiy - 7 years, 1 month ago

Soumava Pal
Feb 17, 2016

Here is my solution. 3435 => 3*4*3*5=180 is our answer.

Thank you!! =D

Pi Han Goh - 5 years, 3 months ago

You are welcome! though I did not understand why you said Thank You!! xD

Soumava Pal - 5 years, 3 months ago

Glad you enjoyed this question, that's why I said thank you because you spent time on my question haha!

Pi Han Goh - 5 years, 3 months ago

@Pi Han Goh – Oh you are welcome, brother! Your questions are always fun to do, often containing much to learn.

Soumava Pal - 5 years, 3 months ago

@Soumava Pal – Hahah thanks! You should post some as well! = )

Pi Han Goh - 5 years, 3 months ago

@Pi Han Goh – I will come back to posting once my finals for the last year of high school get over in March. In the meantime, I am struggling to scrape through chemistry and physics in the final examination. xD

Soumava Pal - 5 years, 3 months ago

Connor Kenway
May 11, 2014

Here's my solution -http://ideone.com/M4tkU1 It outputs 3435 so 3 3 4 5=9 20=180

I dont know how the multiplication symbol vanished between the digits i wrote 3 3 4 5=9 20=180

Connor Kenway - 7 years, 1 month ago

Apparently the star multiplication symbol is used to italicise text

Connor Kenway - 7 years, 1 month ago

TotallyOriginallyCreatedByMe Number

The answer is 180.

3 solutions

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