Four fours
You can make 4 fours equal one like this
1 = 4 / 4 + 4 -4
2 = ?
Can you make a 2? Can you make 3?
See if you can make more.
Can you make 15 at least?
1 = 4 / 4 + 4 -4
2 = ?
Can you make a 2? Can you make 3?
See if you can make more.
Can you make 15 at least?
posted by Ragknot at
3:42 PM
19 Comments:
2=4/((4+4)/4)
3=(4*4-4)/4
of course 2 also = 4/4 + 4/4
4 = (4-4) * 4 + 4
5 = (4+4*4)/4
I could not find 11 or 13.
I hope someone else can.
Clue: Also use sqrt(4)
Is it cheating to use 44?
44/(√4+√4) = 11
This post has been removed by the author.
I don't think 44 is cheating, just something I didn't think of. Good job. We have an 11.
I did not look at the solution yet.
Anyone find a 13? It probably has a 44.
ok, I found 13, it has a "44" in it.
i found 48 unique solutions for solutions up to 92.
19 was the first I gave up on.
To get 19, you must use "4!".
Is anyone working on this puzzle?
Using your clue to find 19...
4!-(4/4)-4=19
(4*3*2*1)-(1)-4=19
24-5=19
19=19
Using the clue for 13...
44/4+sqrt(4)=13
11+2=13
13=13
To tackle the original challenge (excluding the ones already found in the posts)...
6=4/sqrt(4)+sqrt(4)+sqrt(4)
7=4+4-(4/4)
8=(4/4)(4+4)
9=4+4+(4/4)
10=4+4+4-sqrt(4)
12=(4*sqrt(4)*sqrt(4))-4
14=4+4+4+sqrt(4)
15=4*4-(4/4)
Now for the others.
16=4*4*(4/4)
17=4*4+(4/4)
18=4*4+4-sqrt(4)
19=(see my first post)
20=4*4+sqrt(4)+sqrt(4)
21=4!-(4-(4/4))
22=4*4+4+sqrt(4)
23=4!-((4-sqrt(4))/sqrt(4))
24=4*4+4+4
25=4!+((4-sqrt(4))/sqrt(4))
26=4!+sqrt(4)+4-4
27=4!+(4-(4/4))
And I'll stop there for the time being.
This post has been removed by the author.
I could not find all.
Did anyone find 31?
1 44/44
2 Sqrt(4)/Sqrt(4)/Sqrt(4)*4
3 Sqrt(4)/4*fact(4)/4
4 fact(4)*Sqrt(4)*Sqrt(4)/fact(4)
5 4-fact(4)/fact(4)+Sqrt(4)
6 Sqrt(4)*4/Sqrt(4)+Sqrt(4)
7 4*Sqrt(4)-Sqrt(4)/Sqrt(4)
8 4*Sqrt(4)-fact(4)+fact(4)
9 -Sqrt(4)+44/4
10 4+Sqrt(4)*Sqrt(4)+Sqrt(4)
11 44/Sqrt(4)/Sqrt(4)
12 fact(4)/Sqrt(4)/4*4
13 44/4+Sqrt(4)
14 -Sqrt(4)+fact(4)-Sqrt(4)*4
15 44/4+4
16 fact(4)-fact(4)/Sqrt(4)+4
17 fact(4)/fact(4)+4*4
18 44-fact(4)-Sqrt(4)
19 fact(4)-fact(4)/fact(4)-4
20 fact(4)*Sqrt(4)-4-fact(4)
21 fact(4)-Sqrt(4)-4/4
22 fact(4)+Sqrt(4)-Sqrt(4)*Sqrt(4)
23 fact(4)/fact(4)+fact(4)-Sqrt(4)
24 -fact(4)+44+4
25 Sqrt(4)-Sqrt(4)/Sqrt(4)+fact(4)
26 fact(4)+fact(4)-fact(4)+Sqrt(4)
27 fact(4)+4-Sqrt(4)/Sqrt(4)
28 fact(4)-fact(4)+fact(4)+4
29 fact(4)/fact(4)+4+fact(4)
30 Sqrt(4)*Sqrt(4)+Sqrt(4)+fact(4)
32 Sqrt(4)*fact(4)-4*4
34 -Sqrt(4)+fact(4)/Sqrt(4)+fact(4)
35 44/4+fact(4)
36 44-4*Sqrt(4)
38 44-Sqrt(4)-4
40 44-Sqrt(4)-Sqrt(4)
42 -4+44+Sqrt(4)
43 44-Sqrt(4)/Sqrt(4)
44 44-4+4
45 Sqrt(4)/Sqrt(4)+44
46 4*fact(4)/Sqrt(4)-Sqrt(4)
47 fact(4)-Sqrt(4)/Sqrt(4)+fact(4)
48 Sqrt(4)+44+Sqrt(4)
49 Sqrt(4)*fact(4)+Sqrt(4)/Sqrt(4)
50 Sqrt(4)+44+4
52 4+44+4
54 fact(4)*Sqrt(4)+4+Sqrt(4)
56 fact(4)/Sqrt(4)+44
60 44+4*4
62 4*4*4-Sqrt(4)
64 fact(4)-4+44
66 -Sqrt(4)+fact(4)+44
68 fact(4)*Sqrt(4)-4+fact(4)
70 fact(4)*4-fact(4)-Sqrt(4)
72 fact(4)+44+4
74 Sqrt(4)+fact(4)*4-fact(4)
76 -fact(4)+4+fact(4)*4
80 4*fact(4)-4*4
84 44*Sqrt(4)-4
86 -Sqrt(4)+Sqrt(4)*44
88 44/Sqrt(4)*4
90 Sqrt(4)+44*Sqrt(4)
92 fact(4)*Sqrt(4)+44
94 fact(4)*Sqrt(4)*Sqrt(4)-Sqrt(4)
95 4*fact(4)-4/4
96 Sqrt(4)*fact(4)+fact(4)+fact(4)
97 Sqrt(4)/Sqrt(4)+fact(4)*4
98 Sqrt(4)*fact(4)*Sqrt(4)+Sqrt(4)
100 Sqrt(4)*Sqrt(4)+4*fact(4)
4!+4+sqrt(4/.̅4)=31
The bar is supposed to be over the 4, as in a repeating decimal.
Sorry, missed the other gaps.
4!+(sqrt(4)+sqrt(4))/.̅4=33
4!+4+4/.̅4=37
4!+4!-4/.̅4=39
44-sqrt(4/.̅4)=41
4!+4!+sqrt(4/.̅4)=51
44+4/.̅4=53
4!/.̅4+4/4=55
4!/.4-sqrt(4/.̅4)=57
4!/.4+4/4=61
4!/.4+sqrt(4/.̅4)=63
(4^4+4)/4=65
(4!+sqrt(4))/.4+sqrt(4)=67
(44+sqrt(4))/sqrt(.̅4)=69
(4!+4.4)/.4=71
(root(4,.4)+.̅4)/.̅4=73 (where root(4,.4) denotes the .4th root of 4)
(4!/4+4!)/.4=75
(4/.̅4)^sqrt(4)-4=77
(4!+sqrt(4))/sqrt(.̅4)*sqrt(4)=78
(4/.̅4)^sqrt(4)-sqrt(4)=79
(4/.̅4)^(4-sqrt(4))=81
4!/.̅4+4!+4=82
(4/.̅4)^sqrt(4)+sqrt(4)=83
(4/.̅4)^sqrt(4)+4=85
4!*4-4/.̅4=87
(4!+sqrt(4))/.4+4!=89
4!*4-sqrt(4)/.4=91
4!*4-sqrt(4/.̅4)=93
4!*4+sqrt(4/.̅4)=99
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