[Guest]

Hello everyone. This is my first topic on this forum. Please bear me if I make any mistake ;-). I tried to make this question as trickier as possible. Please use spoilers if you already know the answer.

The question is:

Find the mathematical operations labeled A,B,C,D,E,F,G,H so that the following equation comes true:

1 A 2 B 3 C 4 D 5 E 6 F 7 G 8 H 9 = 100

Do not change the sequence of the numbers.

Best of luck!

[Guest]

1+2+3+4+5+6+7+8*9 = 100

sorry

there could be more then one answers but this is the first one I came up with

Edited July 23, 2010 by PVRoot

[Guest]

((1*2)+3)*4*5+6-7-8+9

[Guest]

Unless contradicted by additional specifications by Arsalan, we are given a one to one relation between operators and the capital letters A through H. And, as each operator is between two numbers, we are limited to the binary operators. Unary, ternary, grouping -- brackets, braces, parentheses, etc. -- and most function operators must be excluded, though comparison operators should yet be available.

Still there are several binary operators available:

+ the addition operator

- the subtraction operator

× the multiplication operator (sometimes denoted as * or ∙)

÷ the division operator (sometimes denoted as as /)

^ the exponention, "power", or hyper3 operator (sometimes denoted as ↑ or **)

^^ the tetration or hyper4 operator (sometimes denoted as ↑↑). The notation can be extended to pentation (^^^ or ↑↑↑), hexation (^^^^ or ↑↑↑↑), etc., yet, as we are trying to find an expression to equate to 10, the smallest 2-digit number, the use of hyperoperators which are used to denote huge numbers will probably have no use.

% the modulo function operator (sometimes denoted as mod or modulo). The percent sign can also be used as a unary operator for percent (equivalent to × 1/100), but as has already been specifed unary operators are unusable for this problem.

|| the concatenation operator (Denoted as two parallel pipes is usually used with character strings, yet may be used with numbers. The concatenation of two numbers forms another number. For example, twenty-three concatenated with seven 23||7 forms the number two hundred and thirty-seven 237.)

[Guest]

Unless contradicted by additional specifications by Arsalan, we are given a one to one relation between operators and the capital letters A through H. And, as each operator is between two numbers, we are limited to the binary operators. Unary, ternary, grouping -- brackets, braces, parentheses, etc. -- and most function operators must be excluded, though comparison operators should yet be available.

Still there are several binary operators available:

+ the addition operator

- the subtraction operator

× the multiplication operator (sometimes denoted as * or ∙)

÷ the division operator (sometimes denoted as as /)

^ the exponention, "power", or hyper3 operator (sometimes denoted as ↑ or **)

^^ the tetration or hyper4 operator (sometimes denoted as ↑↑). The notation can be extended to pentation (^^^ or ↑↑↑), hexation (^^^^ or ↑↑↑↑), etc., yet, as we are trying to find an expression to equate to 10, the smallest 2-digit number, the use of hyperoperators which are used to denote huge numbers will probably have no use.

% the modulo function operator (sometimes denoted as mod or modulo). The percent sign can also be used as a unary operator for percent (equivalent to × 1/100), but as has already been specifed unary operators are unusable for this problem.

|| the concatenation operator (Denoted as two parallel pipes is usually used with character strings, yet may be used with numbers. The concatenation of two numbers forms another number. For example, twenty-three concatenated with seven 23||7 forms the number two hundred and thirty-seven 237.)

A correction. The expression is to equate to 100.

[Guest]

1+2*3+4*5-6+7+8*9

[Guest]

1*2*3*4+5+6-7+8*9

[Guest]

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 × 9 = 100

1 + 2 + 3 + 4 + 5 + 6 + 7 + 72 = 100

100 = 100

1 × 2 × 3 + 4 + 5 + 6 + 7 + 8 × 9 = 100

6 + 4 + 5 + 6 + 7 + 72 = 100

100 = 100

1 × 2 × 3 × 4 + 5 + 6 - 7 + 8 × 9 = 100

1 × 2 × 3 × 4 + 5 + 6 - 7 + 8 × 9 = 100

24 + 5 + 6 - 7 + 72 = 100

100 = 100

1 - 2 × 3 - 4 - 5 + 6 × 7 + 8 × 9 = 100

1 - 6 - 4 - 5 + 42 + 72 = 100

100 = 100

As another note, for those who might wish to know, concatenation falls in order of operations with addition and subtraction. Without brackets, this means the operations are performed left to right. Thus, if the sequence began 1 + 2 || 3 + ..., 1 and 2 would be added before being concatenated with 3 giving 33. The modulo operation occurs after division but before addition, subtraction, (and concatenation).

Edited July 23, 2010 by Dej Mar

[Guest]

1 × 2 ^^ 3 × 4 + 5 × 6 + 7 + 8 + 9 = 100

1 × 16 × 4 + 5 × 6 + 7 + 8 + 9 = 100

64 + 30 + 7 + 8 - 9 = 100

100 = 100

For those who are not familiar with tetration:

2^^3 = ³2 = 2²² = 2⁽²²) = 16

Edited July 23, 2010 by Dej Mar

[Guest]

1*2*3+4+5*6-7+8+9=100

[Guest]

1*2*3+4+5*6-7+8+9=100

1 × 2 × 3 + 4 + 5 × 6 - 7 + 8 + 9 =

6 + 4 + 30 - 7 + 8 + 9 =

51 ≠ 100

Your need remember the order of the operations.

For operations at the same level, they are performed top-down (hyperoperations), left-to-right.

There are other operations, but precedence for most operations used in the solution of this puzzle are as follows:

(1) hyperoperations (tetration, exponentiation, roots)

(2) multiplication, division

(3) modulo

(4) addition, subtraction, concatenation

Edited July 23, 2010 by Dej Mar

[Guest]

1 × 2 × 3 + 4 + 5 × 6 - 7 + 8 + 9 =

6 + 4 + 30 - 7 + 8 + 9 =

51 ≠ 100

Your need remember the order of the operations.

For operations at the same level, they are performed top-down (hyperoperations), left-to-right.

There are other operations, but precedence for most operations used in the solution of this puzzle are as follows:

(1) hyperoperations (tetration, exponentiation, roots)

(2) multiplication, division

(3) modulo

(4) addition, subtraction, concatenation

Plain and basic mathematics. Nothing else. Each new number meant another step so there were no hyperoperations. Just simply do the next step from the answer of the one before.

[Guest]

1+2+3+4+5+6+7+8*9 = 100

sorry

there could be more then one answers but this is the first one I came up with

I think Pvroot has it..

Using Order of operations, you would multiply 8*9 1st, with a result of 72.

Then start adding 1+2+3+4+5+6+7 = 28

72+28=100

[Guest]

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 * 9 = 100

[Guest]

Hello everyone. This is my first topic on this forum. Please bear me if I make any mistake ;-). I tried to make this question as trickier as possible. Please use spoilers if you already know the answer.

The question is:

Find the mathematical operations labeled A,B,C,D,E,F,G,H so that the following equation comes true:

1 A 2 B 3 C 4 D 5 E 6 F 7 G 8 H 9 = 100

Do not change the sequence of the numbers.

Best of luck!

Seems there are a lot of possible solutions. An interesting twist to this would be to state that, as each of the letters A-H are different, this implies that the the operators they represent must also be different. Now what do we get?

[superprismatic]

1: 1×2×3×4+5+6-7+8×9=100
2: 1×2×3×4+5+6+7×8+9=100
3: 1×2×3-4×5+6×7+8×9=100
4: 1×2×3+4+5+6+7+8×9=100
5: 1-2×3-4-5+6×7+8×9=100
6: 1-2×3-4+5×6+7+8×9=100
7: 1-2×3+4×5+6+7+8×9=100
8: 1-2+3×4×5-6+7×8-9=100
9: 1-2+3×4×5+6×7+8-9=100
10: 1+2×3×4×5÷6+7+8×9=100 <= note the division here!
11: 1+2×3+4×5-6+7+8×9=100
12: 1+2-3×4-5+6×7+8×9=100
13: 1+2-3×4+5×6+7+8×9=100
14: 1+2+3-4×5+6×7+8×9=100
15: 1+2+3+4+5+6+7+8×9=100

[Guest]

(1*(2+(3*4)))*5 -(6*7)+(8*9) =100

I added parantheses to make it clearer

[Guest]

Hello everyone. This is my first topic on this forum. Please bear me if I make any mistake ;-). I tried to make this question as trickier as possible. Please use spoilers if you already know the answer.

The question is:

Find the mathematical operations labeled A,B,C,D,E,F,G,H so that the following equation comes true:

1 A 2 B 3 C 4 D 5 E 6 F 7 G 8 H 9 = 100

Do not change the sequence of the numbers.

Best of luck!

[Guest]

Hi,

I think I solved it: (/ means 'divided by')

1/2+3x4x5+6+7+8+9=100 (where the conventional Order of Operations does not apply. The operation is executed in the order it appears in the equation.)

Mac42

[Guest]

This one brings the count to 17.

The 15 compiled by superprismatic,

 1:  1×2×3×4+5+6-7+8×9=100

 2:  1×2×3×4+5+6+7×8+9=100

 3:  1×2×3-4×5+6×7+8×9=100

 4:  1×2×3+4+5+6+7+8×9=100

 5:  1-2×3-4-5+6×7+8×9=100

 6:  1-2×3-4+5×6+7+8×9=100

 7:  1-2×3+4×5+6+7+8×9=100

 8:  1-2+3×4×5-6+7×8-9=100

 9:  1-2+3×4×5+6×7+8-9=100

10:  1+2×3×4×5÷6+7+8×9=100   <= note the division here!

11:  1+2×3+4×5-6+7+8×9=100

12:  1+2-3×4-5+6×7+8×9=100

13:  1+2-3×4+5×6+7+8×9=100

14:  1+2+3-4×5+6×7+8×9=100

15:  1+2+3+4+5+6+7+8×9=100

the one I submitted earlier that used tetration,

1 × 2 ^^ 3 × 4 + 5 × 6 + 7 + 8 + 9 = 100

1 × 16 × 4 + 5 × 6 + 7 + 8 + 9 = 100

64 + 30 + 7 + 8 - 9 = 100

100 = 100

For those who are not familiar with tetration:

2^^3 = ³2 = 2²² = 2⁽²²) = 16

and now one that uses simple exponentiation,

1 + 2 ^ 3 + 4 x 5 + 6 + 7 x 8 + 9 = 100

1 + 8 + 20 + 6 + 56 + 9 = 100

100 = 100

[superprismatic]

This one brings the count to 17.

The 15 compiled by superprismatic,

the one I submitted earlier that used tetration,

and now one that uses simple exponentiation,

1 + 2 ^ 3 + 4 x 5 + 6 + 7 x 8 + 9 = 100

1 + 8 + 20 + 6 + 56 + 9 = 100

100 = 100

I neglected to mention that I assume all operations be in the set {×,÷,+,-}. Under that restriction, there are only 15.

[Guest]

I neglected to mention that I assume all operations be in the set {×,÷,+,-}. Under that restriction, there are only 15.

Arsalan stated that he "tried to make this question as trickier [sic] as possible" and he asked us to "Find the mathematical operations ... so that the ... equation comes true". If he wanted to limit the set to {+,-,×,÷}, he should have specified arithemetic operations, which is the set {+,-,×,÷}. Asking for 'mathematic operations' opened our set to the the whole gamut of operations used in mathematics with the exception that there is a one-to-one relation between each of the labels A,B,C,D,E,F,G,H and the operation. As each of these labels were placed between two numbers we were limited to only binary operations, and only those binary operations that can be denoted by a single operator. My first post outlined this, and even opened with "Unless contradicted by additional specifications by Arsalan". As he did not post a contradiction, it should be acceptable to interpret that he indeed meant 'mathematic operations' and not the limited set of 'arithmetic operations'.

Edited July 24, 2010 by Dej Mar

[superprismatic]

Arsalan stated that he "tried to make this question as trickier [sic] as possible" and he asked us to "Find the mathematical operations ... so that the ... equation comes true". If he wanted to limit the set to {+,-,×,÷}, he should have specified arithemetic operations, which is the set {+,-,×,÷}. Asking for 'mathematic operations' opened our set to the the whole gamut of operations used in mathematics with the exception that there is a one-to-one relation between each of the labels A,B,C,D,E,F,G,H and the operation. As each of these labels were placed between two numbers we were limited to only binary operations, and only those binary operations that can be denoted by a single operator. My first post outlined this, and even opened with "Unless contradicted by additional specifications by Arsalan". As he did not post a contradiction, it should be acceptable to interpret that he indeed meant 'mathematic operations' and not the limited set of 'arithmetic operations'.

Sorry, I didn't mean to suggest that those other

operations aren't acceptable. I just wanted to

clarify that my posting made a claim only for the

four arithmetic operations, and that I neglected

to state that fact in the posting.