Colorful consecutive (Part 10)

Computer Science Level 3

$\Large{S=\color{#20A900}1\color{#D61F06}2\color{#3D99F6}3!+\color{#D61F06}2\color{#3D99F6}3\color{#EC7300}4!+\color{#3D99F6}3\color{#EC7300}4\color{magenta}5!+\ldots+\color{#D61F06}7\color{#3D99F6}8\color{#EC7300}9!+\color{#3D99F6}8\color{#EC7300}9\color{magenta}0!}$

Find $S$ $\text{mod}$ $\color{#20A900}1\color{#D61F06}2\color{#3D99F6}3\color{#EC7300}4\color{magenta}5\color{#20A900}6\color{#D61F06}7\color{#3D99F6}8\color{#EC7300}9\color{magenta}0$

The answer is 107086230.

2 solutions

Isaac Buckley
Aug 27, 2015

compski compski

Wolfram saved the day for this one.

Wow! I thought Wolfram Alpha can't evaluate this!

Adam Phúc Nguyễn - 5 years, 9 months ago

Me too, I prayed and wolfram answered!

No "Wolfram|Alpha needs more time to respond to your query..."

Or "Computation timed out. Experimental feature: Try again with more time »"

Or "Computation timed out. No more results available."

The trick is to never loose faith in wolfram and he'll bless you.

Isaac Buckley - 5 years, 9 months ago

Well, may be you can use an elementary way, but it's verrrryyyy long, and I'm lazy.

Adam Phúc Nguyễn - 5 years, 9 months ago

You don't know the power of Wolfram Alpha :P

Arulx Z - 5 years, 9 months ago

Arulx Z
Aug 27, 2015

At current stage, it's very easy and quick to compute the answer directly.

Here's the manual code:

1
2

>>> import math
>>> (math.factorial(123) + math.factorial(234) + math.factorial(345) + math.factorial(456) + math.factorial(567) + math.factorial(678) + math.factorial(789) + math.factorial(890)) % 1234567890

Moderator note:

Simple standard approach.

Here 's a C++ solution. Adding it here for the sake of variety. I envy you since I can't do it directly like that in C++ because of data type range limitations. :|

Prasun Biswas - 5 years, 9 months ago

That's true. I remember banging my head against the walls and using Big Integer (in Java) while others were comfortably using python.