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darani
12-09-2006, 05:05 AM
If you need to square a number (two or three digits) that ends in 5, just use this trick. First, you should know that when any number squared that ends in 5 will always have the last two digits of 25. Then all ya need to do is look at the digits before the 5 and multiply it (them) by the next number higher and put that infront of the 25.

Here's two examples:

1) 35 squared is 3 times 4 (one higher than 3) or 12 and put that in front of 25. Looks like this... 1225

2) 65 squared is 6 times 7 (one higher than 6) or 42 and put that in front of 25. Looks like this .... 4225

darani
12-09-2006, 05:11 AM
"I can add very fast," boasted Billy. "Here, I'll show you. In this calendar, I want you to choose some full week of 7 days. It can be any wekk in any month as long as it has 7 days. Now add the numbers in that week. But don't tell me the sum. Just tell me the number of the first day of the week, and I'll find the sum, too."


Mary chose the week of April 8. Shee added the numbers very carefully. (Did she get 77?)


"I'm ready," said Mary. "I chose the week in April beginning on the eighth."


"Then your sum is 77," said Billy after a breif moment.


"That's right, Billy. How did you add it so fast?"




The key is : If u want the key i need some replies for this to kow it.
ha ha ha

darani
12-09-2006, 05:17 AM
An interesting number is 8. Make a complete table of 8's as started below.

1 x 8 = 8 (0+8 = 8)


2 x 8 = 16 (1+6 = 7)



3 x 8 = 24 (2+4 = 6)



4 x 8 = 32 (3+2 = 5)

5 x 8 = 40 (4+0 = 4)

6 x 8 = 48 (4+8 = 12 ; 1+2 =3)

7 x 8 = 56 (5+6 = 11 ; 1+1 = 2)

8 x 8 = 64 (6+4 = 10 ; 1+0 = 1)



Similarly we can do for 8 x (19,20,....,26)

darani
12-09-2006, 05:26 AM
6 x 2 = 12 (1 + 2 = 3)
6 x 3 = 18 (1 + 8 = 9)
6 x 4 = 24 (2 + 4 = 6)

6 x 5 = 30 (3 + 0 = 3)
6 x 6 = 36 (3 + 6 = 9)
6 x 7 = 42 (4 + 2 = 6)

6 x 8 = 48 (4 + 8 = 12) (1 + 2 = 3)
6 x 9 = 54 (5 + 4 = 9)
6 x 10 = 60 (6 + 0 = 6)



It goes on and on.. try with any number.

darani
12-09-2006, 05:30 AM
Ask your friend to think of any hour on the clock without telling you. Explain that you are going to point randomly to different numbers on the clock while he silently counts up to 20. Tell him to start with the hour that he is thinking of and add one every time you point to a number.



Example: He's thinking of 8:00 so he counts

9 when you point to the first number,

10 when you point to the second number,

etc.

When he gets to 20, he should say, "Stop!", and your pencil will be pointing to the hour that he is thinking of!

How to Do It

As your friend is counting up to 20, you are counting, too. The first seven numbers that you point to can be any numbers on the clock. However, the eighth number must be 12. Then go backwards around the clock until your friend tells you to stop.

darani
12-09-2006, 05:41 AM
Start with the sequence of non-zero digits 123456789. The problem is to place plus or minus signs between them so that the result of thus described arithmetic operation will be 100.






12+3-4+5+67+8+9=100

123+4-5+67-89=100

1+2+34-5+67-8+9=100

12+3-4+5+67+8+9=100

123-4-5-6-7+8-9=100

123+4-5+67-89=100

123+45-67+8-9=100

123-45-67+89=100

12-3-4+5-6+7+89=100

12+3+4+5-6-7+89=100

1+23-4+5+6+78-9=100

1+23-4+56+7+8+9=100

1+2+3-4+5+6+78+9=100





If we put a "-" before 1, we have one more solution:

-1+2-3+4+5+6+78+9=100

Using the "." decimal separation I found another solution:

1+2.3-4+5+6.7+89=100 (solution of my own)








Now we c for the 9 8 7 6 5 4 3 2 1

98-76+54+3+21=100

9-8+76+54-32+1=100

98+7+6-5-4-3+2-1=100

98-7-6-5-4+3+21=100

9-8+76-5+4+3+21=100

98-7+6+5+4-3-2-1=100

98+7-6+5-4+3-2-1=100

98+7-6+5-4-3+2+1=100

98-7+6+5-4+3-2+1=100

98-7+6-5+4+3+2-1=100

98+7-6-5+4+3-2-1=100

98-7-6+5+4+3+2+1=100

9+8+76+5+4-3+2-1=100

9+8+76+5-4+3+2+1=100

9-8+7+65-4+32-1=100

Write the sign "-", three solutions:

-9+8+76+5-4+3+21=100

-9+8+7+65-4+32+1=100

-9-8+76-5+43+2+1=100

With the decimal point:

9+87.6+5.4-3+2-1=100 (solution of my own)

If I "shuffle" the digits there are many solutions. I found some when I was young, for example:

91+7.68+5.32-4=100

98.3+6.4-5.7+2-1=100

538+7-429-13=100

(8x9.125)+37-6-4=100 etc etc etc ..

Solcius
10-02-2008, 09:45 AM
Cool Info. Duke can you shift this topic to educational materials or can any MOD can do this???

sunnyajmal
10-04-2008, 10:56 AM
coolz...