novice needs help

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November 17th 2009, 05:05 AM
mathguy9

novice needs help

I am needing help with the following six puzzles. Any and all help would be greatly appreciated.

1. Here is a long division sum, showing all the work, and the result. Simple, right? The sum works out exactly, with no remainder. The slight complication is, that all the numbers have been replaced with letters on a random basis. However, one letter always represents the same number. Can you reconstruct the original sum?

(The problem is ADGAAHD divided by AB) (CDEFG is the answer)

______CDEFG_________________

AB ADGAAHD
AJK
-------------------------------------------
AKA
AAG
---------------------------------------------
FA
JF
------------------------------------------------
AGH
AEE
--------------------------------------------------
FD

2. 6-2
18

8-7
84

12-4
?

3. Can you figure out the reasoning of these numbers, and replace the question mark with the correct number?

5 3 8 7
12 15 49 56
3 9 4 12
18 27 36 ?

4.Take a look at these digital "watches". By cracking the logic that connects them, you should be able to figure out what time should be on watch number five.

15.14.01
12.18.00
08.26.58
03.42.55
??.??.??

5.Thirty-six

Sixty-four

Seventy-two

Twenty-five

Eighty-one

What is the odd number out?

6. Can you figure out the logic behind these number "squares" and find the number that replaces the question mark?

9 6 5 10 4 6 ? 5
4 2 3 7 8 11 12 7

(Think of each set of four numbers as a square. 9 = top left, 4 = bottom left, 6 = top right, 2 = bottom right, and so on, it might help to write them down.)

Thank you again for any and all help

mathguy
November 17th 2009, 07:34 PM
Soroban

Hello, mathguy9!

I hope I interpreted #1 correctly . . .

Quote:

1. Here is a long division sum, showing all the work, and the result.
The divison works out exactly with no remainder.
All the digits have been replaced with letters on a random basis.
However, one letter always represents the same number.
Can you reconstruct the original division?

. . $\begin{array}{cccccccccc} & & & & & C & D & E & F & G \\ & & & -- & -- & -- & -- & -- & -- & -- \\ A & B & | & A & D & G & A & A & H & D \\ & & & A & J & K \\ & & & -- & -- & -- \\ & & & & A & K & A \\ & & & & A & A & G \\ & & & & -- & -- & -- \\ & & & & & & F & A \\ & & & & & & J & F \\ & & & & & & -- & -- \\ \end{array}$
. . . . . . . . . . . . . . . . . . . . . $\begin{array}{cccccccccc} & & & & & & A & G & H \\ & & & & & & A & E & E \\ & & & & & & -- & -- & -- \\ & & & & & & & & F & D \\ & & & & & & & & F & D \\ & & & & & & & & -- & -- \end{array}$

. . $\begin{array}{ccc} A\:=\:1 & & F \:=\:7 \\ B \:=\:9 && G \:=\:4 \\ C\:=\:8 && H\:=\:0 \\ D\:=\:6 && J\:=\:5 \\ E\:=\:3 && K\:=\: 2 \end{array}$

. . $\begin{array}{cccccccccc} & & & & & 8 & 6 & 3 & 7 & 4 \\ & & & -- & -- & -- & -- & -- & -- & -- \\ 1 & 9 & | & 1 & 6 & 4 & 1 & 1 & 0 & 6 \\ & & & 1 & 5 & 2 \\ & & & -- & -- & -- \\ & & & & 1 & 2 & 1 \\ & & & & 1 & 1 & 4 \\ & & & & -- & -- & -- \\ & & & & & & 7 & 1 \\ & & & & & & 5 & 7 \\ & & & & & & -- & -- \\ \end{array}$
. . . . . . . . . . . . . . . . . . . . . $\begin{array}{cccccccccc} & & & & & & 1 & 4 & 0 \\ & & & & & & 1 & 3 & 3 \\ & & & & & & -- & -- & -- \\ & & & & & & & & 7 & 6 \\ & & & & & & & & 7 & 6 \\ & & & & & & & & -- & -- \end{array}$
November 17th 2009, 08:17 PM
Wilmer

Quote:

Originally Posted by mathguy9

5.Thirty-six
Sixty-four
Seventy-two
Twenty-five
Eighty-one
What is the odd number out?

Question really means: which number does not belong ?
Easy...LOOK carefully!
November 18th 2009, 07:06 AM
Soroban

Hello, mathguy9!

I think I have #4 . . .

Quote:

4. Take a look at these digital "watches".
By cracking the logic that connects them, you should be able
to figure out what time should be on watch number five.

. . $\begin{array}{ccccc}\text{H} && \text{M} && \text{S} \\ \hline 15 & : & 14 & : & 01 \\ 12 & : & 18 & : & 00 \\ 08 & : & 26 & : & 58 \\ 03 & : & 42 &:& 55 \\ ? &:& ? &:& ? \end{array}$

The consecutive differences of the Hours suggest this sequence:

. $\begin{array}{c|ccccccccc}\text{Hours} & 15 && 12 && 8 && 3 && {\color{blue}\text{-}3} \\ \hline \text{Difference} && \text{-}3 && \text{-}4 && \text{-}5 && {\color{blue}\text{-}6} \end{array}$

The consecutive differences of the Minutes suggest this sequence:

. $\begin{array}{c|ccccccccc}\text{Minutes} & 14 && 18 && 26 && 42 && {\color{blue}74} \\ \hline \text{Difference} && +4 && +8 && +16 && {\color{blue}+32} \end{array}$

The consecutive differences of the Seconds suggest this sequence:

. $\begin{array}{c|ccccccccc}\text{Seconds} & 01 && 00 && 58 && 55 && {\color{blue}51} \\ \hline \text{Difference} && \text{-}1 && \text{-}2 && \text{-}3 && {\color{blue}\text{-}4} \end{array}$

$\begin{array}{cccccccc}\text{The final time is:} & -3 & : & 74 &:& 51 \\ \text{which convets to:} & 09 &:& 74 &:& 51 \\ \text{and finally:} & 10 &:& 14 &:& 51 \end{array}$
November 18th 2009, 08:19 AM
bbeckett

Quote:

3. Can you figure out the reasoning of these numbers, and replace the question mark with the correct number?

5 3 8 7
12 15 49 56
3 9 4 12
18 27 36 ?

The answer is 48. The numbers are in four squares of four numbers, so the first square is:

5 3 let this be: a b
12 15 c d

You will find that in each square, c = (a-1)*b and d=a*b.

In the final square, 4*12=48
November 18th 2009, 06:36 PM
mathguy9

you guys are so great. Thank you so much for all your help.
November 30th 2009, 11:09 AM
wonderboy1953

For the sixth question

The answer is 9.

Here's the pattern:

6*4 - 2*9 = 24 - 18 = 6
10*3 - 7*5 = 30 - 35 = -5
6*8 - 4*11 = 48 - 44 = 4
5*12 - 7*9 = 60 - 63 = -3

To caution, patterns are useful but sometimes more than one pattern can match up with the problem at hand so keep a sharp eye open for that.
November 30th 2009, 01:46 PM
Soroban

Hello, mathguy9!

I have five answers to problem #5.

Quote:

5. . $\begin{array}{c}\text{Thirty-six} \\ \text{Sixty-four} \\ \text{Seventy-two} \\ \text{Twenty-five} \\ \text{Eighty-one} \end{array}$ . . What is the odd number out?

36 - the only number with 9 divisors.

64 - the only number whose sum of digits is even.

72 - the only number which is not a square.

25 - the only number less than 33.

81 - the only number greater than 77.