# 24

Dejection
Posers and Puzzles 18 Jun '08 07:13
1. 18 Jun '08 07:131 edit
Many of you may have done something similar before.

You are given four numbers, and you must use each number exactly once. You may only use multiplication, division, addition and subratction and parentheses. You must come up with expression that equals 24. 'Joining' numbers is not allowed, for example if you had a 1 and a 3, you may not simply join then to make 13, or 31. Exponentials are no allowed. This includes roots and recipricals.

So the challenge is, make 24 from these sets of numbers
1 2 3 4
1 2 3 5
1 2 3 6
1 2 4 5
1 2 4 6
1 2 5 6
1 3 4 5
1 3 4 6
1 3 5 6
1 4 5 6
2 3 4 5
2 3 4 6
2 3 5 6
2 4 5 6
3 4 5 6

Out of those, 1346 is by far the most difficult. I'll post the people who have solved each one next to it.

2. 18 Jun '08 07:1913 edits
1 x 2 x 3 x 4 = 24
(1 + 2) x (3 + 5) = 24
(2 + 3 - 1) x 6 = 24
(5 + 2 - 1) x 4 = 24
(6 + 2) x (4 - 1) = 24
(5 - 2 + 1) x 6 = 24
(5 + 4 - 1) x 3 = 24
I solve this later (I hope)
6 x 3 + 5 + 1 = 24
-
(3 + 4 + 5) x 2 = 24
6 x 3 + 2 + 4 = 24
6 x 5 - 2 x 3 = 24
6 x 5 - 2 - 4 + 24
- I have to go now

(many edits because I first solved 1, then 2 etc.)
3. 18 Jun '08 07:431 edit
i wonder if i can remember all of them

i know i can remember 1346 but the others i havnt done for a while

what about mking 41 using 2, 6, 8, 10 and 11 still remember?

EDIT: i wonder if 1,3,4,6 and 1,4,5,6 use the same technique or is there an easier way
4. 18 Jun '08 08:03
Originally posted by banx99
i wonder if i can remember all of them

i know i can remember 1346 but the others i havnt done for a while

what about mking 41 using 2, 6, 8, 10 and 11 still remember?

EDIT: i wonder if 1,3,4,6 and 1,4,5,6 use the same technique or is there an easier way
I only don't know the technique
5. 18 Jun '08 08:21
using 1 3 4 6:

6 / (1 - 3/4)
= 6 / (1/4)
= 24

another one to try: 5 5 5 1
6. 18 Jun '08 08:51
using 2, 6, 8, 10 and 11, see how high you can get starting from 24
in other words, get 25, 26, 27 etc etc
so far im past 50
7. TheMaster37
Kupikupopo!
18 Jun '08 10:25
To quote one of the regulars here:

"SOLV'D".
8. 18 Jun '08 10:361 edit
Originally posted by TheMaster37
To quote one of the regulars here:

"SOLV'D".
mine or fianchettos?

EDIT: any help would be nice, i cant find an answer for 76
9. TheMaster37
Kupikupopo!
19 Jun '08 12:30
Originally posted by banx99
mine or fianchettos?

EDIT: any help would be nice, i cant find an answer for 76
I'm referring to the 24 problem ðŸ™‚

(1 - 1/5) * 5 is the one for 1, 5, 5, 5
10. 19 Jun '08 12:47
I suppose you mean (5-1/5)*5
11. TheMaster37
Kupikupopo!
22 Jun '08 10:10
Originally posted by Dejection
I suppose you mean (5-1/5)*5
Indeed I do ðŸ™‚

I gave this to one of my classes the other day. They have never been that quiet in the entire year :p
12. 23 Jun '08 00:16
still wondering why no one can seem to solve for 76 using 2,6,8,10 and 11