2006 puzzle

Of the numbers below, 5 of them add up to 2006, and only those five. The question is... which ones? No need to cheat by writing a program to try all possible combinations, there is an easier way

413 448 336 351 308 476
392 378 483 364 441 329
386 315 420 428 455 343
469 463 371 406 399 322

The only way i can think of is trial and error, but that will take forever.

Originally posted by perihelion
No need to cheat by writing a program to try all possible combinations, there is an easier way

I know, just get somebody to write one for you.

i had the solution through trail and error but all i can remeber is 322

Originally posted by Knight Square
The only way i can think of is trial and error, but that will take forever.

I'm thinking going by the last numbers might work. Get two pairs which each add to a number with a 0 at the end then add one that has a 6 at the end. Otherwise it would be trial and error.

I decided I am too lazy to actually try it though.

See if you can find something these numbers have in common. Most of them anyway...

Originally posted by perihelion
See if you can find something these numbers have in common.

A piece of cake. They all have three digits. 😏 🙄

Originally posted by perihelion
See if you can find something these numbers have in common. Most of them anyway...

They're Harshad numbers. Well, most of them anyway.

Also, they're all composites but one.

Originally posted by Bowmann
They're Harshad numbers. Well, most of them anyway.

Also, they're all composites but one.

And they are all even, except nine of them!

Originally posted by ThudanBlunder
And they are all even, except nine of them!

An odd conclusion 😕

Originally posted by Bowmann
[b]They're Harshad numbers. Well, most of them anyway.
b]

What are Harshad numbers? I suppose I could search on Google but an answer here might interest many who are following this thread.

Originally posted by perihelion
No need to cheat by writing a program to try all possible combinations, there is an easier way

I dunno...writing a program is pretty damn easy.

Originally posted by Mixo
What are Harshad numbers? I suppose I could search on Google but an answer here might interest many who are following this thread.

Those divisible by the sum of their digits, and a source of great joy to many.

Google loads rather quickly through modern connections.

351, 378, 386, 428, 463
no i didn't use trial and error

Originally posted by aginis
351, 378, 386, 428, 463
no i didn't use trial and error

And we have a winner!

For those still trying to figure it out, Bowmann's observation that most of them are composites is on the right track. Keep looking in this direction for something more specific.