Transhumanist
 Senior Boarder
Posts: 69 
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Here is a problem by J.A.H. Hunter on expressions for successive integers.
Today we have just one '4' and two '7's.' Using these, all three but no other figures, together with any regular mathematical signs, you have to make up expressions for the successive numbers from '1' upwards. As a simple example, you can express the number 21 as 7*(7-4).
You can use pluses, minuses, multiplication signs, division signs, brackets, powers, roots, decimals both regular and repeating, concatenation, factorials, and summation signs.
Use ROOT(n,m) as the nth root of m and SQRT as the square root. 7*SQRT(4)=49 and .ar=.aaaa... Use SUM(a,b,f(i)) as the summation function where a is the lower limit, b is the upper limit, and f(i) is a function of i. a and b must be expressions containing only some or all the integers(4,7,7) and if f(i) contains any numbers they must be selected 4,7, and 7. Remember that 4, 7, and 7 must be used in the entire expression.
b
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Javid
 Senior Boarder
Posts: 67
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Using just myself, here are 1-18:
1=(7/7)^4 2=(7/7)*SQRT(4) 3=4-(7/7) 4=4*7/7 5=4+7/7 6=7/.7-4 7=7/.7r-SQRT(4) 8=7/.7-SQRT(4) 9=SQRT(7/.7r)^(SQRT(4)) 10=SQRT(7/.7r)!+4 11=7/.7r+SQRT(4) 12=7/.7+SQRT(4) 13=7/.7t+4 14=7/.7+4 15=4!-7/.7r 16=7+7+SQRT(4) 17=4!-SQRT(7*7)
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Javid
Senior Boarder
Posts: 67
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Only using SUM for 19,22,26,29,37,39... (and 5 or less i)
19=SUM(7,7,i+i+i)-SQRT(4) 20=SQRT(4)*7/.7 21=4*7-7 22=SUM(4,SQRT(7*7),i) 23=4!-7/7 24=4!+7-7 25=4!+7/7 26=SUM(7-7,4,i*(i+i)-i!) 27=4!+SQRT(7/.7r) 28=SQRT(4)*(7+7) 29=7+SUM(4,7,i) 30=(SQRT(7/.7r))!+4! 31=4!+SQRT(7*7) 32=SQRT(SQRT(4^(7/.7))) 33=4!+7/.7r 34=4!+7/.7 35=4*7+7 36=4*7/.7r 37=SUM(4,7,i+i)-7 38=4!+7+7 39=SUM(7,7,i+i+i+i+i)+4 40=4*7/.7
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Jim
Expert Boarder
Posts: 80
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'better':
26=SUM((7-4)!,7,i+i)
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Atraxani
Expert Boarder
Posts: 83
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26=SUM((7-4)!,7,i+i) 39=SUM(4,7/.7r,i) 40=4*7/.7 41=SQRT(SUM(7/7,4,i!*i!+i!*i!-i!*i*i)) 42=7^SQRT(4)-7 43=SUM(7/7,4,i!+i) 44=SUM(4,SQRT(7*7),i+i) 45=7*7-4 46=4+SUM(7,7,i+i+i+i+i+i) [Not sure if 46=SUM(7/7,4,i+i/.i) is legit] 47=7*7-SQRT(4) 48=SUM(7,SQRT(7)^SQRT(4),i*i-i/i) 49=SQRT(7*7)^SQRT(4) 50=SUM(7-4,7,i+i)
I'm done now.
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garyncurtis
Expert Boarder
Posts: 87
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SPOILER
1 = sqrt(4)-7/7 2 = sqrt(4)+7-7 3 = 4-7/7 4 = 4+7-7 5 = 4+7/7 6 = 7/.7-4 7 = (7+7)/sqrt(4) 8 = 7/.7-sqrt(4) 9 = sqrt(4)+sqrt(7*7) 10 = 7+7-4 11 = 4+sqrt(7*7) 12 = 7+7-sqrt(4) 13 = 4+7/.7r 14 = 4+7/.7 15 = 7/(.7*sqrt(.4r)) 16 = sqrt(4)+7+7 17 = 4!-sqrt(7*7) 18 = 4+7+7 19 = sum(4,7,i+i/i)-7 20 = sqrt(4)*7/.7 21 = 4*7-7 22 = sum(4,sqrt(7*7),i) 23 = 4!-7/7 24 = 4!+7-7 25 = 7/(.4*.7) 26 = sum(4,sqrt(7*7),i+i/i) 27 = 4!+sqrt(7/.7r) 28 = sqrt(4)*(7+7) 29 = sum(4,7,i)+7 30 = 7!/(7*4!) 31 = 4!+sqrt(7*7) 32 = (sqrt(sqrt(4)))^(7/.7) 33 = 4!+7/.7r 34 = 4!+7/.7 35 = 7+4*7 36 = 4*(7/.7r) 37 = sum(4,7,i+i)-7 38 = 4!+7+7 39 = sum(sqrt(4),7,i+i+i-7) 40 = 4*7/.7
Please reply to ilan at cedara dot com
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quest2006
Senior Boarder
Posts: 79
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You should have at least done 51, since it is so easy. (the next few are not bad either) 51=7*7+SQRT(4) 52=SUM((7-4)!,7,i+i+i+i) 53=7*7+4
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JohnBStone
Expert Boarder
Posts: 80
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A few more... 55=SUM(7,7+4,i+i/i+i/i) 56=(7+7)*4
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