Combine 3, 3, 5 & 7 to get 24

Question

Using operators plus, minus, multiplied by and divide by, and as many brackets as you want, can you do a formula which uses 3, 3, 5 and 7 to make 24?

Each number must be used and can only be used once (so there will be two 3's).

So, for example, (3x7)+3 makes 24, but this isn't valid because the 5 wasn't used.

I don't know if this is possible, btw! It's in a game I'm playing.

Well, I noticed that $${\large 57-33=24}.$$ Does this break any rules? — Mr Pie, Jul 26 '18 at 10:33
@user477343 Definitely a good answer https://puzzling.stackexchange.com/questions/5555/hidden-in-plain-sight-by-what-method-do-these-images-hide-a-prime-number/5566#5566 — Raystafarian, Jul 27 '18 at 06:26

score 26 · Accepted Answer · answered Jul 26 '18 at 08:55

26

Well, I tried to solve it the hard way (using double fractions) but actually it's quite easy.

(3 * 5 - 7) * 3 = (15 - 7) * 3 = 8 * 3 = 24

answered Jul 26 '18 at 08:55

Paul Palmpje

536
5
4

2

Indeed, by brute-force search, this is the only formula up to commutative transformation. – LegionMammal978 Jul 26 '18 at 12:15

Kevin · Answer 2 · 2018-07-26T17:49:52.903

16

Heh, how about:

(3 XOR 5) x (3 XOR 7)

... yes, yes, I know XOR's not allowed. Poor XOR. Nobody ever invites him.

edited Jul 26 '18 at 17:49

answered Jul 26 '18 at 15:50

Kevin

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1
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Nice twist in this answer! – Paul Palmpje Jul 26 '18 at 16:32
Could someone please explain this answer? I know XOR as a logic gate but I don't understand how can it be used here? – EducatedEnt Jul 06 '20 at 12:53
@defectedWBC - XOR on numbers treats each bit independently. 3 XOR 5 is: 0011 XOR 0101, which is 0110, or 6. Likewise, 3 XOR 7 is: 0011 XOR 0111 = 0100, or 4. If you're on a windows machine, you can go into Calculator and set it to Programmer mode, and perform XOR's as well. – Kevin Jul 06 '20 at 13:03

score 7 · Answer 3 · edited Jul 26 '18 at 13:51

7

what about this one?

using factorials of 3
$7+5+3!+3! = 24$

edited Jul 26 '18 at 13:51

Saeïdryl

3,040
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28

answered Jul 26 '18 at 12:37

K. Dumre

77
3

2

Nice but the question lists specific operators. The factorial is not one of them. I solved one of these using binomials once. Although this does not use new operators it does rely on the placement of the numbers and should not be accepted. – Paul Palmpje Jul 26 '18 at 12:44

score 7 · Answer 4 · edited Jul 27 '18 at 05:27

We can use as many brackets as we want, and Wikipedia states

Square brackets, as in [π] = 3, are sometimes used to denote the floor function, which rounds a real number down to the next integer.

So I will use square brackets [] to denote the floor function.

$$([5 \div 3]+7) \times 3 = (1+7) \times 3 = 8 \times 3 = 24$$

If we massage the rules a little more, and can put numbers in different positions, we can use Falling Factorial notation, where

$$(x)_n = x(x-1)(x-2)\ \cdot \cdot \cdot (x-n+1) = \frac{x!}{(x-n)!}$$

$$[(5)_3 \div 7] \times 3 = \big[\frac{5!}{(5-3)!} \div 7 \big] \times 3 = [60 \div 7] \times 3 = 8 \times 3 = 24$$

Unfortunately, there is no way to use combinations to get the given input to 24.

argh, it was going so well. – Max Williams Aug 06 '18 at 07:45 — Max Williams, Aug 06 '18 at 07:45

score 5 · Answer 5 · edited Jul 30 '18 at 07:44

5

When we

combine 3 and 3 it makes 33

and when we

combine 5 and 7 it makes 57

then

subtract 57-33

it will give the answer 24

edited Jul 30 '18 at 07:44

Glorfindel

28,033
9
96
142

answered Jul 30 '18 at 07:19

Nikita garg

55
1

score 4 · Answer 6 · answered Jul 27 '18 at 08:49

4

How about:

3 + 3 + 5 + 7 + 6 = 24

Explanation:

Each number must be used and can only be used once, but the rules don't say other numbers cannot be used!

answered Jul 27 '18 at 08:49

Masked Man

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1
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Hmm, I guess i did miss an "only" there. – Max Williams Aug 06 '18 at 07:46

animalknox · Answer 7 · 2018-07-27T14:11:24.183

2

I also thought about :

$3 * (7 - 5) ^ 3$

Breaks the rule but hey

edited Jul 27 '18 at 14:11

answered Jul 27 '18 at 14:03

animalknox

29
2

score -3 · Answer 8 · edited Jul 26 '18 at 13:50

-3

please check it

$(3*3*5)-(7*3) = 45-21 = 24$

edited Jul 26 '18 at 13:50

Saeïdryl

3,040
13
28

answered Jul 26 '18 at 12:52

Nikita garg

55
1

5

It's got an extra 3, so it's breaking the rules. – Bernat Jul 26 '18 at 12:59

score -3 · Answer 9 · edited Jul 26 '18 at 17:23

-3

Seems pretty straight forward, sorry I don't know how to hide it:

(5x7) - (3x3) = 35 - 9 = 24

edited Jul 26 '18 at 17:23

Joe-You-Know

9,565
2
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76

answered Jul 26 '18 at 16:46

CrossRoads

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Sorry, this is wrong: 35 - 9 = 26, not 24. – Fabio says Reinstate Monica Jul 26 '18 at 17:00
2

Sure, engineer, I can do math! Out of practice it seems. – CrossRoads Jul 26 '18 at 17:03

score -3 · Answer 10 · answered Jul 30 '18 at 06:27

-3

check it 3!+3!+5+7 =6+6+12 =24

answered Jul 30 '18 at 06:27

Nikita garg

55
1

1

Welcome to Puzzling! This uses an operator (!) which is not allowed according to the rules in the question. – Glorfindel Jul 30 '18 at 06:52

Combine 3, 3, 5 & 7 to get 24

10 Answers10