Maths powers failing me...

April 24, 2006 7:31 AM

Maths question: How can you make 25 using only the numbers 2,4,6,8?

A friend of mine has been stumped by this - and as a mathmatical illiterate so am I. Apparently you can use each number once and there is no requirement to use all of them. I am assuming there is some sort of cunning trick at the heart of this...

posted by prentiz to science & nature (38 comments total)

(8 x 3) + (2/2) ?
posted by bhance at 7:34 AM on April 24, 2006

although I suppose the 2/2 violates the 'use once' clause ... (slinks back to coffee-less morning. $@#%)
posted by bhance at 7:36 AM on April 24, 2006

ummm....where'd the 3 come from?
posted by pooya at 7:38 AM on April 24, 2006

4*6 + log(8+2 )= 24+1 = 25
though technically that's ln(8+2)/ln(10) and you're using extra numbers...
posted by cardboard at 7:40 AM on April 24, 2006

(2/8) * (4+6) = 2.5

almost?
posted by poppo at 7:41 AM on April 24, 2006

Ha. 3. Wow. Jesus.

I'm seriously going for coffee before I walk off a cliff.
posted by bhance at 7:43 AM on April 24, 2006

((4 + 6)/8)^2 = 25/16

Does that count?
posted by malp at 7:43 AM on April 24, 2006

I think we need to know what kinds of operations are allowed. Only addition, subtraction, multiplication and division? Or other stuff, like logs above? How about roots and exponentials? Does sqrt count as a use of 2?
posted by miagaille at 7:44 AM on April 24, 2006

sqrt(8-(6/2))^4
posted by gleuschk at 7:53 AM on April 24, 2006

4! + (8-6)/2 = 25
posted by pooya at 7:53 AM on April 24, 2006

Usually in these types of questions only the four basic operations are allowed, but if we can use fancy stuff here's a suggestion:

4! = 24
8-6 = 2
2/2 = 1
24+1 = 25
posted by miagaille at 7:54 AM on April 24, 2006

There is no solution using only normal (+-/*) operators.
posted by public at 7:59 AM on April 24, 2006

ok i've thought of a good trick (if, say you're doing this on a piece of paper or a napkin):

((4*8) - 6) * 2 = 52

Now turn the piece of paper upside down
posted by poppo at 8:04 AM on April 24, 2006

Are you sure it's not a transcription error? If 6 becomes 5, then:

5 + 2 = 7
8 * 4 = 32
32 - 7 = 25
posted by cribcage at 8:14 AM on April 24, 2006

4! + sin(8) = 24.989358247 (radians)
or
4! + cos(2) = 24.999390827 (degrees)

or even better
4! + cos(8-2-6) = 25
posted by handee at 8:28 AM on April 24, 2006

ummm....where'd the 3 come from?

6/2?
posted by mdn at 8:42 AM on April 24, 2006

ie, 8 x (6/2) + (4/4)
posted by mdn at 8:43 AM on April 24, 2006

square root of (6/2)^2 + (8-4)^2, i.e., the Pythagorean theorem
posted by ancientgower at 9:14 AM on April 24, 2006

er, ancientgower - doesn't that make 5?
posted by handee at 9:50 AM on April 24, 2006

how about w/ just 2,4,6?
6 upside down and reversed is a 9
9 + 4^2 = 25
posted by treeshade at 9:50 AM on April 24, 2006

handee can drop his last cos for an extra factorial, should one wish to avoid trig. Otherwise, I'd have suggest something like poppo's method.
posted by edd at 9:52 AM on April 24, 2006

(6+(2/8))*4 == 25
posted by Steven C. Den Beste at 9:53 AM on April 24, 2006 [1 favorite]

S C D B!
posted by TimeFactor at 10:00 AM on April 24, 2006

(6+(2/8))*4 == 25

A solution fiendishly clever in its intricacies.
posted by loquax at 10:28 AM on April 24, 2006

crap! i spent ten minutes staring at .25, just knowing that that was related to the solution. curse you, steven c. den beste!
posted by poppo at 10:42 AM on April 24, 2006

Poppo just made the 25th comment, and no math was involved. My brain, she a'splode!
posted by Oddly at 10:59 AM on April 24, 2006

Here's another one: ((2+8)/.4)
posted by inkyz at 12:16 PM on April 24, 2006

related to SCDB, (6+4)*(2/8)
posted by dness2 at 12:19 PM on April 24, 2006

Here's another one: ((2+8)/.4)
posted by inkyz at 12:16 PM PST on April 24 [!]

No

related to SCDB, (6+4)*(2/8)
posted by dness2 at 12:19 PM PST on April 24 [!]

No
posted by poppo at 12:27 PM on April 24, 2006

A few years ago I wrote a quick perl script to brute-force the answer to a very similar puzzle. It's here, if anyone's interested.
posted by hades at 6:33 PM on April 24, 2006

poppo, inkyz's solution is correct (as are pooya's and, as noted above, SCBD's).
posted by rob511 at 7:27 PM on April 24, 2006

I don't think inkyz's solution technically counts, since he diviced 4 by 10 before he used it. SCDB's solution is "the best one" because it only uses multiplication, division, addition, and subtraction.
posted by muddgirl at 8:22 PM on April 24, 2006

The problem with inkyz's solution is that 6 is not used.
posted by nomis at 8:35 PM on April 24, 2006

nomis, according to prentiz's question, "there is no requirement to use all of the [four numbers]." And muddgirl, if using a decimal point doesn't count (even though the challenge didn't mention notation), then pooya's use of 4! (or 4 • 3 • 2 • 1) fails too, even though both their solutions were quite creative.

prentiz?
posted by rob511 at 12:09 AM on April 25, 2006

poppo, inkyz's solution is correct

um, inkyz uses ".4". this is NOT the same as "4"

even if it was, what is the answer to inkyz solution? -15 ?


(as are pooya's and, as noted above, SCBD's).

pooya's, yes if we are allowing all kinds of operands

we still haven't heard from prentiz, but for my money, Steven is the only one who got it.
posted by poppo at 6:17 AM on April 25, 2006

And mine.
4! + cos(8-2-6) = 25
Nobody said anything about "no trig".
posted by handee at 3:49 AM on April 26, 2006

Although obviously Steven wins.
posted by handee at 3:49 AM on April 26, 2006

Yay! So where's my check mark?
posted by Steven C. Den Beste at 11:38 AM on April 26, 2006