This document presents several mathematical facts and tricks. Some examples include: Armstrong numbers where the sum of each digit raised to the power of the number of digits equals the number; vampire numbers where parts of the number multiplied equal the full number; and tricks for multiplying by 11 or calculating squares ending in 5 quickly. Puzzles involving measuring water quantities and crossing a bridge within a time limit are also presented. The document aims to showcase interesting properties and relationships in numbers.

1. MAGICAL FACTS
ABOUT MATH
PRESENTED BY:
NEHA SHARMA
TAFADZWA GONERA

2. ARMSTRONG NUMBER
 153 is an Armstrong number
because
 153=1³+5³+3³
 Some other Armstrong numbers
are:
 370,371,407

3. STRANGE FACTS ABOUT 666
 666=6³+6³+6³+6+6+6
 666=2²+3²+5²+7²+11²+13²+17²

4. VAMPIRE NUMBERS
 1260 is a vampire number
 With 21 and 60 as fangs
 Since 21 × 60 = 1260.
 Others are: 1395=15 × 93
 1435=41 × 35
 1530=51 × 30

5. Numeric Palindrome with 1's
1x1=1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

6. Sequential Inputs of 9
9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998001
9999 x 9999 = 99980001
99999 x 99999 = 9999800001
999999 x 999999 = 999998000001
9999999 x 9999999 = 99999980000001
99999999 x 99999999 = 9999999800000001
999999999 x 999999999 = 999999998000000001

7. Number 2519
2519 Mod 2 = 1
2519 Mod 3 = 2
2519 Mod 4 = 3
2519 Mod 5 = 4
2519 Mod 6 = 5
2519 Mod 7 = 6
2519 Mod 8 = 7
2519 Mod 9 = 8
2519 Mod 10 = 9

8. Trick
 Step1: Think of a number below 10.
 Step2: Double the number you have
thought.
 Step3: Add 6 with the getting result.
 Step4: Half the answer, that is divide it by
2.
 Step5: Take away the number you have
thought from the answer, that is, subtract
the answer from the number you have
thought.

9. ANSWER IS 3 FOR THE TRICK

10. RULE 11
 To multiply any two digit number by 11:
 For this example we will use 54.
 Separate the two digits in you mind
(5__4).
 Notice the hole between them!
 Add the 5 and the 4 together (5+4=9)
 Put the resulting 9 in the hole 594. That's
it! 11 x 54=594

11. RULE 11
 If the result of the addition is greater than
9
 You only put the "ones" digit in the hole
and carry the "tens" digit from the
addition.
 For example 11 x 57 ... 5__7 ... 5+7=12 ...
put the 2 in the hole and add the 1 from
the 12 to the 5 in to get 6 for a result of
627 ... 11 x 57 = 627

12. MAGIC OF NUMBER 9

13. MAGIC OF NUMBER 9

14. MAGIC OF NUMBER 9

15. SNAKE EATS ITS OWN TAIL
• Choose any two digits number and for each
one reverse the digits and subtract the
smaller number from the larger.
• In each case the difference is divisible by 9
and the sum of the digits of the difference is
always 9.

16. Age Calculation Tricks:
 Step1: Multiply the first number of the
age by 5.
 Step2: Add 3 to the result.
 Step3: Double the answer.
 Step4: Add the second digit of the
number with the result.
 Step5: Subtract 6 from it.

17. TO FIND THE REMAINDER

18. PUZZLE
 You are at a fountain and have with you a
three gallon jug and a five gallon jug. The
jugs have no markings on the sides. How
would you be able to measure out exactly
one gallon of water?

19. SOLUTION
First, fill up the 3 gallon jug to the top, and
pour it into the 5 gallon jug.
5 - 3 = 2 free gallons left in the 5 gallon jug.
Now, fill up the 3 gallon jug again, and pour as
much as you can into the 5 gallon jug.
3 - 2 = 1 gallon of water left in the 3 gallon
jug.
Finally, pour the remaining gallon of water
from the 3 gallon jug into your 1 gallon jug.
Result = 1 gallon of water!

20. EASY SQUARING
 If you want to find the square of 45.
 You will first have to multiply 4 (4 +1),
that is 4 X 5, which is equal to 20
 Then multiply 5 with 5, which is 25.
 The answer is 2025.
 Now, you can employ this method to
multiply all numbers ending with 5.

21. Bridge Crossing Puzzle:
 A, B, C and D wants to cross the bridge at
night. They have only one torch light with
them. Only two can cross the bridge at a
time. They need torch light to cross the
bridge. Each of them walks at a different
speed. A needs 1 minute, B needs 2 minutes,
C needs 5 minutes and D needs 10 minutes.
 A pair must walk together at the rate of the
slower person.
 How these people can cross the bridge within
17 minutes?

22. Solution:
 First A and B walks across the bridge, it takes
2 minutes.
 A walks back with the torch light, which
takes 1 minute.
 Then C and D walk on the bridge, which
takes 10 minutes.
 B comes back with the torch light, it takes 2
minutes.
 Finally A and B walks across the bridge,
which takes 2 minutes.
 Total = 2 + 1 + 10 + 2 + 2 = 17 minutes.

23. FINGER MATH FOR 9 TABLE

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