[Guest]

I'd like to extend previous sak_ikos's puzzle

By using the numbers 1, 3, 4, and 6 make all numbers from 1 to 25. It is allowed to use only following mathematical operations: +, −, ×, ÷ and brackets. Factorials, exponents, rounding and other math operations are not allowed. Each number must be used once and only once. Decimal points are not allowed at any place. Mathematical operations can be used any number of times.

Solution exists for each number 1,2,3,4,...,25. For some numbers more solutions exist.

Edited June 17, 2010 by Hugo

[Guest]

(3+4-6)*1=1

3+4-6+1=2

3/6*4+1=3

6-4+3-1=4

(6+3-4)*1=5

6-4+3+1=6

(6+1)(4-3)=7

6+4-3+1=8

6*4/3+1=9

4*(3+1)-6=10

(6-3)*4-1=11

6+4+3-1=12

(6+4+3)*1=13

6+4+3+1=14

6*3-4+1=15

4*(6-3+1)=16

3*4+6-1=17

3*4+6*1=18

3*4+6+1=19

(6+4)(3-1)=20

6*3+4-1=21

6*3+4*1=22

6*3+4+1=23

24 has been solved by you...

(6+1)*4-3=25

[Guest]

(6+1-3)/4=1

(6+3-1)/4=2

3*(6-1-4)=3

6+3-1-4=4

(6-1)*(4-3)=5

6+1+3-4=6

(6+4-3)*1=7

6+4+1-3=8

(6-3)*(4-1)=9

(1+4)*(6/3)=10

13+4-6=11

6+4+3-1=12

(4+3+6)*1=13

4+3+6+1=14

16+3-4=15

16*(4-3)=16

16+4-3=17

(3*4+6)*1=18

3*4+6+1=19

4*6-3-1=20

(4*6-3)*1=21

4*6+1-3=22

6*3+4+1=23

6!/[3!*(1+4)]=24

(6+1)*3+4=25

[Guest]

(3 * 4 / 6) - 1 = 1

(1 * 3 * 4) / 6 = 2

(3 * 4 / 6) + 1 = 3

6 + 3 - 4 - 1 = 4

(6 / 3) + 4 - 1 = 5

(6 * 1 / 3) + 4 = 6

(6 / 3) + 4 + 1 = 7

(6 * 4 * 1) / 3 = 8

(6 * 4 / 3) + 1 = 9

(1 + 3) * 4 - 6 = 10

(6 - 1) * 3 - 4 = 11

6 + 3 + 4 - 1 = 12

(6 + 3 + 4) * 1 = 13

6 + 4 + 3 + 1 = 14

(4 - 1) * 3 + 6 = 15

(3 - 1) * 6 + 4 = 16

(6 + 1) * 3 - 4 = 17

(3 * 4 * 1) + 6 = 18

(6 - 1) * 3 + 4 = 19

(3 + 1) * 6 - 4 = 20

(4 + 1) * 3 + 6 = 21

(3 + 1) * 4 + 6 = 22

(6 - 1) * 4 + 3 = 23

6 / (1 - (3 / 4)) = 24

(6 + 1) * 3 + 4 = 25

[unreality]

I'd like to extend previous sak_ikos's puzzle

By using the numbers 1, 3, 4, and 6 make all numbers from 1 to 25. It is allowed to use only following mathematical operations: +, −, ×, ÷ and brackets. Factorials, exponents, rounding and other math operations are not allowed. Each number must be used once and only once. Decimal points are not allowed at any place. Mathematical operations can be used any number of times.

Solution exists for each number 1,2,3,4,...,25. For some numbers more solutions exist.

here we go...

1 = (6 - 4) / (3 - 1)

2 = 1 / (6/(3*4)) or more simply 2 = 3 * 4 * 1 / 6

3 = 4 + 1 - (6/3)

4 = 4 * (6/3 - 1)

5 = 6/3 - 1 + 4

6 = 1 * (4-3) * 6

7 = 1 + 6/3 + 4

8 = 6 + 4 + 1 - 3

9 = (6*4)/3 + 1

Oops I have to go but I will resume

[Guest]

1. (3 + 4 - 6) x 1

2. 1 + 3 + 4 - 6

3. 3 x (6 - 4 - 1)

4. (6 - 4) x (3 - 1)

5. (6 - 1) x (4 - 3)

6. 6 x 4 / ( 3 + 1)

7. 3 x 4 - 6 + 1

8. 6 + 4 + 1 - 3

9. (6 / 3) x 4 + 1

10. (4 + 1) x (6 / 3)

11. (6 - 3) x 4 - 1

12. 4 + 6 - 1 + 3

13. (6 - 3) x 4 + 1

14. 1 + 3 + 4 + 6

15. (6 - 3) x (4 + 1)

16. (3 - 1) x 6 + 4

17. (6 + 1) x 3 - 4

18. (3 x 4) + 6 x 1

19. (3 x 4) 6 + 1

20. (6 + 4) x (3 - 1)

21. (4 - 1) x 6 + 3

22. (1 + 3) x 4 + 6

23. (6 x 3) + 4 + 1

24. ??

25. (6 + 1) x 4 - 3

[Guest]

the next three are trivial:

26= -1+3+(4*6)

27= 3/1+(4*6)

28= 1+3+(4*6)

[Guest]

( 3 * 4 ) / 6 - 1 = 1

1 + 3 + 4 - 6 = 2

(3 * 4 ) / 6 + 1 = 3

( ( 6 / 3 ) - 1 ) * 4 = 4

(3 * 4 ) - 6 - 1 = 5

6 - 3 - 1 + 4 = 6

( 6 * 4 ) / 3 - 1 = 7

( 6 * 4 ) / 3 * 1 = 8

( 6 * 4 ) / 3 + 1 = 9

( 6 / 3 ) * ( 4 + 1 ) = 10

( 6 - 1 ) * 3 - 4 = 11

6 + 4 + 3 - 1 = 12

( 6 * 3 ) - 4 - 1 = 13

( 6 * 3 ) - 4 * 1 = 14

( 6 * 3 ) - 4 + 1 = 15

4 * ( 6 - 3 + 1 ) = 16

( 3 * 4 ) + 6 - 1 = 17

( 3 * 4 ) + 6 * 1 = 18

( 3 * 4 ) + 6 + 1 = 19

6 * 4 - 3 - 1 = 20

6 * 4 - 3 * 1 = 21

6 * 4 - 3 + 1 = 22

6 * 3 + 4 + 1 = 23

No need answer .... = 24

( 6 + 1 ) * 4 - 3 = 25