Solve ABC = A! + B! + C! The Factorial Digits Sum Puzzle!

I'm thinking of a three digit number where the number exactly equals the sum of the factorial of each digit. What is the number?

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[GretgorPooper]

I failed to solve this problem because I thought ABC meant AxBxC.

[tommykornfeld]

Don’t you need a bar above the ABC to signify that they represent digits in a number, not a product?

[jasertio]

The problem is poorly presented as is. When writing out ABC, he should have used notation to specify that it meant concatenation and not multiplication of A, B, and C.

[AnTran-ievq]

I thought the puzzle was A*B*C and A, B, C are numbers, not digits :) Oh, well.
And in the case of my puzzle, the answer would be 3, 3, 4 only

[NestorAbad]

Nice! Now... Let's try to generalize to numbers of 4 digits, 5 digits... And so on!

[marcinziajkowski]

I thought between ABC are implicit multiple signs. So my solution is 3*3*4 = 3! + 3! + 4! => 36 = 36

[deoxal]

Should have explained that it was A*100 + B*10 + C = A! + B! + C! and not A*B*B = A! + B! + C!

[harshsharma]

As soon as I saw this question 145 came to my mind because I wrote a program to find this number two years back :p

[erik_forsmoo]

After you've found that one of the digits has to be 5, you can just check which of the factorials can give you a sum which includes the digit 5. Since 1! + 4! = 25, you can now try out those numbers and discover that they fit the puzzle.

[SiavashRahnama]

Hi Presh. Thanks for the great videos. In this video, you practically tried every possible answer to get the solution. While it "gets" to an answer, it doesn't showcase any special trick. I myself preferred a way that gets there without trying every possible digit. A way to solve it mathematically rather than brute force. Thanks again for the great channel

[priyeshgupta]

145
Solved this before watching video😁🤟

[rahulbramhankar]

I tried solving the other way by multiplying ABC 😂😂😂

[shizanketsuga]

In the final stage shouldn't it be 15C and 1B5? In one case B would be unknown, in the other C, not B in both cases.

[jacksainthill]

So many complaints in the comments, but the video title clearly states that this is a *_digits_* sum puzzle.
Nice wok, Presh, thank you.

[eurovisioncyan]

Before the video:




7!=5040, so A, B, C<7
6!=720, so A, B, C<6
3(4!)=72, so one of them has to be 5
3(5!)=360, so A is not equal to 5
Try B as 5
Only way possible to get B=5 is 3!+4!+5!
So B is not equal to 5
Therefore, C is
List all the ways that A!+B!'s sum's last digit=5
1!+4!=25 and it's the only way
1!+4!+5!=145
So A=1, B=4, C=5

[geronbreuer]

At the end a Michael Jackson Quote from" heal the world" :D👍🏼

[LaVieDeReine]

You need to signify concatenation. Writing ABC is a primary school level error.

[ahmadafifverdiansyaputra]

I thought ABC is A • B • C...

At least this is the interesting one
🙂

[devondevon]

If A or B or C is not unique then 4 3 3 as 4 x 3 x 3 =36 and 4! +3! +3! =36 . I thought A B C means A x B x C, not three separate digits

[aznable]

I thought the question was A*B*C=A!+B!+C!. lul