# 2006 puzzle

perihelion
Posers and Puzzles 28 Jul '06 17:20
1. 28 Jul '06 17:20
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
2. 29 Jul '06 01:12
The only way i can think of is trial and error, but that will take forever.
3. 29 Jul '06 01:465 edits
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.
4. 29 Jul '06 02:34
i had the solution through trail and error but all i can remeber is 322
5. AThousandYoung
All My Soldiers...
29 Jul '06 03:18
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.
6. 29 Jul '06 05:04
See if you can find something these numbers have in common. Most of them anyway...
7. 29 Jul '06 05:572 edits
Originally posted by perihelion
See if you can find something these numbers have in common.
A piece of cake. They all have three digits. 😏 🙄
8. Bowmann
Non-Subscriber
29 Jul '06 16:22
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.
9. 29 Jul '06 17:011 edit
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!
10. Bowmann
Non-Subscriber
29 Jul '06 17:08
Originally posted by ThudanBlunder
And they are all even, except nine of them!
An odd conclusion 😕
11. 29 Jul '06 18:44
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.
12. BigDoggProblem
29 Jul '06 19:38
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.
13. Bowmann
Non-Subscriber
29 Jul '06 21:54
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.