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5

5

5+5-5+5-5+5-5+5-5

-5 -5

5

1 = (5 - 5)*5 + 5/52 = [(5+5)/5]*(5/5)3 = (5+5)/5 + 5/54 = (5+5+5+5)/55 = (5/5)*(5/5)*56 = (5*5)/5 + 5/57 = (5*5 + 5 + 5)/58 = (5+5+5)/5 + 59 = (5*5 - 5)/5 + 510 = (5*5 + 5*5)/5

(5/5)*(5/5)=1 (5/5)+(5/5)=2 (5+5+5)/5=3 sqrt(5+5)-(5/5)=4 sqrt(5+5)*(5/5)=5 sqrt(5+5)+(5/5)=6 5+((5/5)/5)=7 5+.5+(5*.5)=8 (5+5)-(5/5)=9 sqrt(5+5)+sqrt(5+5)=10 5+5+(5/5)=11 (5*5*.5)-.5=12 (5*5*.5)+.5=13 ((5!/5)*.5)+5=17 (5!/5)*sqrt(5*5)=19 5*5-sqrt(5*5)=20 (55/5)/.5=22 (5!/5)-(5/5)=23 (5!/5)-(5-5)=24 (5!/5)+(5/5)=25 (5*5)+(5/5)=26 (55*.5)-.5=27 (55*.5)+.5=28 (5!/5)+sqrt(5*5)=29 5*5+sqrt(5*5)=30

1+8+5+4+5+5-5-5-5-5-5-5-5-5-5 = -17

5

25 different ways: 20, 20, 20, 20, 5 20, 20, 20, 10, 10, 5 20, 20, 20, 10, 5, 5, 5 20, 20, 20, 5, 5, 5, 5, 5 20, 20, 10, 10, 10, 10, 5 20, 20, 10, 10, 10, 5, 5, 5 20, 20, 10, 10, 5, 5, 5, 5, 5 20, 20, 10, 5, 5, 5, 5, 5, 5, 5 20, 20, 5, 5, 5, 5, 5, 5, 5, 5, 5 20, 10, 10, 10, 10, 10, 10, 5 20, 10, 10, 10, 10, 10, 5, 5, 5 20, 10, 10, 10, 10, 5, 5, 5, 5, 5 20, 10, 10, 10, 5, 5, 5, 5, 5, 5, 5 20, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5 20, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 20, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 10, 10, 10, 10, 10, 10, 10, 10, 5 10, 10, 10, 10, 10, 10, 10, 5, 5, 5 10, 10, 10, 10, 10, 10, 5, 5, 5, 5, 5 10, 10, 10, 10, 10, 5, 5, 5, 5, 5, 5, 5 10, 10, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5 10, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Not all numbers are possible and for some numbers there are several solutions. Here are some examples: 0: (5x5)-(5x5) 1: (5:5)+5-5 2: (5:5)+(5:5) 3: (5+5+5):5 4: [(5x5)-5]:5 5: [(5-5)x5]+5 6: [(5x5)+5]:5 7: [(5+5):5]+5 10: 5+5+5-5 11: (5:5)+5+5 15: (5x5)-5-5 20: 5+5+5+5 24: (5x5)-(5:5) 25: (5x5)+5-5 26: (5x5)+(5:5) 30: [(5:5)+5]x5 35: (5x5)+5+5 45: [(5+5)x5]-5 50: (5x5)+(5x5) 55: [(5+5)x5]+5 75: (5+5+5)x5 120: (5x5x5)-5 130: (5x5x5)+5 625: 5x5x5x5

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5(5 + 5/5) or (5/5+5)*5 and 5*5 + sqrt[5*5] and 5*5 + (5 squared)/5

1953125

50 50 25 25 25 25 20 x .05 50 25 25 50 25 5 5 5 5 5 50 5 5 5 5 5 5 5 5 5 5 25 25 25 5 5 5 5 5 25 25 5 5 5 5 5 5 5 5 5 5 25 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

A. 5+5-5= 10-5= 5 ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... B. 5+5-5= 5+0= 5 ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... C. 5+5-5= -5+5+5= -5+10= 5

6

5 + 5 + 5 - 5 + 5 + 5 - 5 + (5 x 0) = 15

9*5=45 or 5+5+5+5+5+5+5+5+5=45 or1*5*9=45

Note that the reason there exists a technique called multiplication is so that we do not have to perform tedious and lengthy series of addition such as the one you have presented. So, you have given us 24 of the number 5 to add. 24 x 5 = 120. (Addition form) 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 120

5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45, the shorter version is 5*9.

5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 55

The trick here is to multiply by the value 1, but express it as (5 - √5)/(5 - √5). This forms a difference of squares on the bottom, eliminating the radical:(1 + √5) / (5 + √5)= (1 + √5)(5 - √5) / (5 + √5)(5 - √5)= (5 - √5 + 5√5 - 5) / (25 - 5√5 + 5√5 - 5)= 4√5 / 20= √5 / 5

3x5 5+5+5

5/100