Download Mysterious Primes - Australian Teacher

Maths Mysteries
Contents
The Missing 8
page 2
Multiples of 9
page 3
Magic Multiples
page 4
Mysterious Primes page 5
Amazing Number 2 520 page 6
Pi (π)
page 7
Some Fun With Pi (π)
page 8
Zeno’s Achilles Paradox page 9
Palindromic Primes
page 10
Magic Number 143
page 11
Making 100 with 1-9
page 12
Prime Fact
page 13
Mind-boggling Arrangements
Puzzling Patterns
page 15
Happy Numbers
page 16
Pervasive Palindromes
page 17
Times Equals Plus
page 18
Years in Reverse
page 19
Solutions
page 14
page 20
1
Maths Mysteries
The Missing 8
Without 8
12
12
12
12
345
345
345
345
679
679
679
679
x
x
x
x
With the 8
9 = 111 111 111
18 = 222 222 222
27 = 333 333 333
36 = 444 444 444
and notice…
123
123
123
123
456
456
456
456
789
789
789
789
x
x
x
x
9 = 1 111 111 101
18 = 2 222 222 202
27 = 3 333 333 303
36 = 4 444 444 404
and notice…
12 345 679 x 999 999 999 =
12 345 678 987 654 321
123 456 789 x 999 999 999 =
123 456 788 876 543 211
Challenge:
Complete these
1.
2.
3.
4.
5.
Without the 8.
12
12
12
12
12
345
345
345
345
345
679
679
679
679
679
x
x
x
x
x
45
54
63
72
81
=
=
=
=
=
With the 8.
6.
7.
8.
9.
10.
123
123
123
123
123
456
456
456
456
456
789
789
789
789
789
x
x
x
x
x
45
54
63
72
81
=
=
=
=
=
The ‘without 8’ pattern continues below:
12 345 679 x 90 = 1 111 111 110
12 345 679 x 99 = 1 222 222 221
12 345 679 x 108 = 1 333 333 332
Fill in the answers to questions 11-16.
11. 12 345 679 x 117 =
12. 12 345 679 x 126 =
13. 12 345 679 x 135 =
14. 12 345 679 x 144 =
15. 12 345 679 x 153 =
16. 12 345 679 x 162 =
The ‘with the 8’ pattern continues below:
123 456 789 x 90 = 11 111 111 010
123 456 789 x 99 = 12 222 222 111
123 456 789 x 108 =13 333 333 212
Now fill in the answers to questions 17-22:
17. 123 456 789 x 117 =
18. 123 456 789 x 126 =
19. 123 456 789 x 135 =
20. 123 456 789 x 144 =
21. 123 456 789 x 153 =
22. 123 456 789 x 162 =
2
Maths Mysteries
Multiples of 9
987
987
987
987
987
654
654
654
654
654
321
321
321
321
321
X
X
X
X
X
9 = 8 888 888 889
18 = 17 777 777 778
27 = 26 666 666 667
36 = 35 555 555 556
45 = 44 444 444 445
Challenge:
1.
What do you notice about the first and last digits of the product?
2.
3.
4.
5.
987
987
987
987
Complete these:
654
654
654
654
321
321
321
321
X
X
X
X
54
63
72
81
=
=
=
=
3
Maths Mysteries
Magic Multiples
142
142
142
142
142
142
857
857
857
857
857
857
X
X
X
X
X
X
1
2
3
4
5
6
=
=
=
=
=
=
142
285
428
571
714
857
857
714
571
428
285
142
Challenge:
1.
2.
3.
4.
5.
6.
What do you notice about the digits in the products?
Does the pattern continue? To see if it does work this one out yourself (you may use a
calculator if you wish):
142 7 X 7 =
Using these same digits, consider this: 142 + 857. What is the answer?
Now try this: 14 + 28 + 57 =
Write out, in words, the smallest number you can make using the digits 1, 4, 2, 8, 5 qnd
7.
Write out, in words, the largest number you can make using the digits 1, 4, 2, 8, 5 qnd
7.
4
Maths Mysteries
Mysterious Primes
Every prime number except for 2 and 3 is evenly divisible by 6 if you
either subtract 1 from it or add 1 to it.
13-1=12 and 12 is divisible by 6.
17+1=18 and 18 is divisible by 6.
Challenge:
1.
2.
3.
4.
5.
6.
Does the rule work for the prime 37? Test it.
Does the rule work for the prime 41? Test it.
Does the rule work for the prime 43? Test it.
Does the rule work for the prime 47? Test it.
Does the rule work for the prime 59? Test it.
What prime number gives a quotient of 4 after
by 6?
7. What prime number gives a quotient of 5 after
divided by 6?
8. What prime number gives a quotient of 2 after
by 6?
9. What prime number gives a quotient of 3 after
divided by 6?
10. What prime number gives a quotient of 9 after
by 6?
1 is added to it and the result is divided
1 is subtracted from it and the result is
1 is added to it and the result is divided
1 is subtracted from it and the result is
1 is added to it and the result is divided
5
Maths Mysteries
Amazing Number 2 520
The number 2 520 can be divided by 1 and 2 and 3 and 4 and 5 and 6
and 7 and 8 and 9 and 10.
Challenge:
1.
2.
3.
4.
Write down the first ten factors of 2 520.
7 and 8 are factors of 2 520; does that mean that 56 is a factor of 2 520?
28, 35, 42. Which of these are not factors of 2 520?
11, 12, 14, 15, 16, 18, 20, 21, 22, 24.
Seven of these ten numbers are also factors of 2 520. Which ones are they?
5. Can 5 040 be divided by 1 and 2 and 3 and 4 and 5 and 6 and 7 and 8 and 9 and 10?
6. 2 520 divided by 2 equals 1 260. Which of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10
are not factors of 1 260?
6
Maths Mysteries
Pi (π)
Pi is the number of times the diameter of a circle goes into the circumference.
That is, C/D = π or π = C/D.
We often use 22/7 as the value of π but this is only an approximation.
22/7 = 3.14285714268……. . But π = 3.14159265859……. .
Down through the years many attempts have been made to calculate an exact value of π.
1 650 BC Ancient Egyptians: π = 3.16
150 AD Ptolomy: π = 3.1416
1 561 Roomen: π = 3.14…..(15 decimal places)
1 600 Van Ceulen: π = 3.14…..(35 decimal places)
1 699 Sharp: π = 3.14…..(71 decimal places)
1 701 Machin: π = 3.14…..(100 decimal places)
1 853 Rutherford: π = 3.14…..(440 decimal places)
1 873 Shanks: π = 3.14…..(527 decimal places)
1 945 computer: π = 3.14…..(2 000 decimal places)
2 000 computer: π = 3.14…..(2 00 million decimal places)
Challenge:
1. The Ancient Egyptians thought that π equalled 4 X (8/9)2.
Use your calculator to write this value correct to five decimal places.
2. Archimedes (287 BC – 212 BC) thought that π was between 223/71 and 22/7.
Was he right?
3. Construct a circle with radius 10 cm (diameter = 20 cm). Using a piece of string or cotton
thread measure the circumference as accurately as possible. Is the circumference about 63 cm?
7
Maths Mysteries
Some Fun With Pi (π)
Here is a fun way you can learn the value of
π to many decimal places.
All you need do is to make up a sentence consisting of words with certain numbers of letters.
The number of letters in a word will match the number in the appropriate place in π.
Example
When the famous professor Max Planck (a German) was teaching quantum mechanics to his
university class one of the students wrote:
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.
All of thy geometry, Herr Planck, is fairly hard……
3.14159265358979323846264….
This student was able to easily memorise π to twenty-two decimal places!
Challenge:
See how many π decimal places you can learn by making up your own sentence (don’t worry if
it’s not twenty-two!).
8
Maths Mysteries
Zeno’s Famous Paradox
Zeno of Elea (490 BC – 425 BC) is known for his intriguing paradoxes.
The best known of these concerns the runner Achilles who is not able to run down
a tortoise.
According to Zeno a tortoise, given a head start by Achilles, can not be overtaken
by the runner.
Zeno reasons that in the time it takes Achilles to reach the point at which the
tortoise started (point A) the tortoise has moved on to point B.
When Achilles reaches B the tortoise has moved on to C.
When Achilles reaches C the tortoise has moved on to D, and so on.
Challenge:
1. Suppose Achilles runs 100m in 10 seconds and the tortoise runs 100 metres in 1 000
seconds. The tortoise has a 10m start, at point A.
How long will it take Achilles to reach point A?
2. Upon Achilles’ arrival at A the tortoise arrives at B; how far (from A) has the tortoise
progressed?
3. How long will it take Achilles to get from A to B?
4. By how far (ie from B to C) has the tortoise progressed when Achilles arrives at B?
5. How long will it take Achilles to get from B to C?
9
Maths Mysteries
Palindromic Primes
A palindrome is a word that reads the same backwards as it does forwards.
Examples are: dad, mum, madam, sees, etc.
A palindromic number is a number that reads the same backwards as it does forwards.
Examples are: 111, 2002, 3443, 51215, etc.
A palindromic prime is a prime number that reads the same backwards as it does forwards.
Remember, a prime number has only two factors, itself and 1.
A number is not a prime if it can be divided evenly (ie without a remainder) by any of the
primes, that is 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.
Challenge:
1. There is only one palindromic prime with an even number of digits. What is it?
All the numbers below are palindromic but only some are palindromic primes.
Write yes if the number is a palindromic prime and no if it is not.
2.
3.
4.
5.
6.
7.
8.
9.
10.
101
111
121
131
141
151
161
171
181
10
Maths Mysteries
Magic Number 143
When the multiples of 143 are multiplied by 7 curious results are
obtained.
Challenge:
1. Complete the table.
143 X 1
Multiples of
143
143
143 X 2
286
143 X 3
429
143 X 4
143 X 5
143 X 6
143 X 7
143 X 8
143 X 9
X7
Multiples of
143
X7
143 X
10
143 X
27
143 X
38
143 X
47
143 X
54
143 X
60
143 X
73
143 X
87
143 X
99
2. Are the numbers in the first x 7 column palindromic (that is, do they read the same
backwards?
3. Are the numbers in the second x 7 column palindromic (that is, do they read the same
backwards?
11
Maths Mysteries
Making 100 with 1-9
Can you place plus or minus signs between all the different digits 1-9 to make
100? (the digits must be in order, 1-9)
Here is one way to do it:
1+2+34-5+67-8+9=100
And another…..
And another…..
12+3-4+5+67+8+9=100
123-4-5-6-7+8-9=100
Challenge:
There are eight more solutions.
Can you find any of them?
Note: If you can discover just one more solution you are doing very well!
12
Maths Mysteries
Prime Fact
The first two prime numbers are 2 and 3.
All other primes are either one less than or one greater than a multiple
of 6, which is the product of 2 and 3.
Example 1
Which prime (or primes) is either one less or one more than the first multiple of six?
Answer: 5 is one less, 7 is one more.
Example 2
Which prime (or primes) is either one less or one more than the third multiple of six?
Answer: 17 is one less, 19 is one more.
Example 3
Which prime (or primes) is either one less or one more than the sixth multiple of six?
Answer: 37 is one more.
Challenge:
Complete the table.
1st multiple of 6
2nd multiple of 6
3rd multiple of 6
4th multiple of 6
5th multiple of 6
6th multiple of 6
7th multiple of 6
8th multiple of 6
9th multiple of 6
10th multiple of 6
11th multiple of 6
12th multiple of 6
13th multiple of 6
14th multiple of 6
15th multiple of 6
16th multiple of 6
17th multiple of 6
18th multiple of 6
19th multiple of 6
20th multiple of 6




















6
12
18
24
30
36
Prime
Numbers
5 and 7
11 and 13
17 and 19
23
29 and 31
37
13
Maths Mysteries
Mind-boggling Arrangements
If you select two cards from a pack of 52 how many ways can you arrange them?
Let’s suppose the cards are the King of Hearts and the Queen of Diamonds.
The arrangements are: KH, QD and QD, KH.
So, for two cards, there are two arrangements, that is 2 X 1.
If we add an extra card, the Jack of Spades, we would have these arrangements:
KH, QD, JS; KH, JS, QD; QD, KH, JS; QD, JS, KH; JS, KH, QD; JS, QD, KH.
So for three cards there are six arrangements, or 3 X 2 X 1.
Now add the Ace of Clubs, making four cards.
The possible arrangements are:
AC, KH, QD, JS; AC, KH, JS, QD; AC, QD, KH, JS; AC, QD, JS, KH; AC, JS, QD, KH;
AC, JS, KH, QD; + six arrangements beginning with KH + six arrangements beginning with
QD + six arrangements beginning with JS.
So for four cards there are twenty-four arrangements, or 4 x 3 x 2 x 1.
How many arrangements could we make with all 52 cards?
The answer is 52 x 51 x 50 x 49 x 48 …….. x 1.
This number is unimaginably large.
It would take light approximately 9 billion billion billion billion billion billion years to travel 52 x
51 x 50 x 49 x 48 …….. x 1 kilometres!
Challenge:
(you will need your calculator for these)
1.
2.
3.
4.
In how many ways could you arrange 5 cards?
In how many ways could you arrange six children?
In how many ways could you arrange the eleven players on a soccer team?
Find the pattern and complete the table below.
Number of
cards
Number of
possible
arrangements
1
2
3
4
5
6
7
8
9
10
1
2
6
24
120
720
2X1
3X2
4X6
5 X 24
6 X 120
14
Maths Mysteries
Puzzling Patterns
Sometimes maths reveals mysterious patterns.
Challenge:
Complete the four patterns below.
1.
2.
42 = 16
342 = 1156
3342 = 111556
33342 = 11115556
333342 = 1111155556
3333342 = 111111555556
33333342 =
333333342 =
= 111111111555555556
= 11111111115555555556
3.
72 = 49
672 = 4489
6672 = 444889
66672 = 44448889
666672 = 4444488889
6666672 = 444444888889
66666672 =
666666672 =
= 444444444888888889
= 44444444448888888889
4.
7 X 9 = 63
77 X 99 = 7623
777 X 999 = 776223
7777 X 9999 = 77762223
77777 X 99999 = 7777622223
777777 X 999999 =
= 77777762222223
92 = 81
992 = 9801
9992 = 998001
99992 = 99980001
999992 = 9999800001
9999992 =
= 99999980000001
5. Fill in the missing number.
42 + 72 + ? = 92
6. Fill in the missing number.
342 + 672 + ? = 992
15
Maths Mysteries
Happy Numbers
To find out if a number is a happy number add the squares of its digits. Then do the same to
the resultant number; keep adding the squares of the digits in the resultant numbers. You will
either reach a cycle (or loop) consisting of the numbers 4-16-37-58-89-145-42-20 or you will
end up at number 1.
Starting numbers that end up at 1 are called Happy Numbers.
12 = 1
One is a happy number.
22 = 4;
42 = 16; 12 + 62 = 37;
+ 0 = 4 and the loop continues.
32 + 72= 58;
52 + 82 = 89;
82 + 92 = 145; 12 + 42 + 52 = 42;
42 + 22 = 20;
22
2
Two is not a happy number.
52 = 25;
2
4 = 16;
22 + 52 = 29; 22 + 92= 85;
1 + 62 = 37; 32 + 72= 58;
2
Five is not a happy number.
72 = 49;
42 + 92 = 97;
92 + 72 = 130;
82 + 52 = 89; 82 + 92 = 145; 12 + 42 + 52 = 42;
52 + 82 = 89 and the loop continues.
12 + 32 + 02 = 10;
42 + 22 = 20;
22 + 02 = 4;
12 + 02 = 1
Seven is a happy number.
Challenge:
Which of the following numbers are happy numbers?
258
356
40 129
78 999
42 315 186
71 406 333
16
Maths Mysteries
Pervasive Palindromes
Take any positive number of two digits or more, reverse the digits, and add to the original
number.
If the resultant number is not a palindrome, repeat the procedure with the sum until the
resultant number is a palindrome.
For example, start with 87 or 88 or 89.
Applying this process we obtain:
87
87 + 78 = 165
165 + 561 = 726
726 + 627 = 1353
1353 + 3531 = 4884
88
88 is a palindrome
89
89 + 98 = 187
187 + 781 = 968
968 + 869 = 1837
until finally, after 24 steps, becomes 8813200023188
Challenge:
Use the reversal method above to find the palindromes generated by the following numbers.
(the maximum number of reversals and additions required is four).
1.
6.
11.
16.
32
2. 49
3. 301
4. 75
5. 426
687
7. 432
8. 92
9. 47
10. 297
5304
12. 371
13. 59
14. 2082
15. 546
3549
17. 284
18. 4871
19. 2906
20. 4830
21. The smallest number that will not produce a palindrome in this way (no matter how many
reversals) and additions, is 196.
Or is it? Try it and see!
17
Maths Mysteries
Times Equals Plus
There is an infinite number of numbers that have the same value whether added or multiplied.
They follow this pattern:
3 + 1½ = 3 x 1½ = 4½
4 + 11/3 = 4 x 11/3 = 51/3
5 + 1¼ = 5 x 1¼ = 6¼
Challenge:
1.
Complete the table.
3 + 1½
4 + 11/3
5 + 1¼
10 + 11/9
2.
= 3 x 1½
= 4 x 11/3
= 5 x 1¼
--------------------------------------------------------------= 10 x11/9
= 111/9
Now complete the table.
996 + 11/995
1000 + 11/999
3.
= 4½
= 51/3
= 6¼
= 996 x 11/995
---------------------------------------------= 1000 x 11/999
= 9971/995
= 10011/999
There is only one number that can be added to itself and multiplied by itself with the
same result. Can you find this number?
18
Maths Mysteries
Years in Reverse
The year 2002 was a palindrome.
So was the year 1991.
Did you realise the previous occurrence of two palindromic years in one person’s lifetime was
the years 999 and 1001!
The next such pair will be 2992 and 3003.
So this happens about once every 1000 years.
The next palindromic year will be 2112.
Universal Day of Symmetry
8:02 PM on February 20th, 2002 was a very unique time and date.
It may be written as 20:02, 20/2, 2002 (24 hour clock system).
Without the punctuation it becomes:
2002 2002 2002
which is three palindromic numbers in a row.
It is also a palindromic sentence because the three numbers taken together are the same when reversed.
Challenge:
Three of the following also form palindromic sentences.
Write them out as above.
a) 10:01 AM on January 10, 1001
b) 8:08 AM on August 8, 808
c) 11:11 AM on November 11, 1111
d) 9:19 AM on September 19, 919
e) 9:12 PM on December 21, 2112
19
Maths Mysteries
Solutions
The Missing 8
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
555 555 555
666 666 666
777 777 777
888 888 888
999 999 999
5 555 555 505
6 666 666 606
7 777 777 707
8 888 888 808
9 999 999 909
1 444 444 443
1 555 555 554
1 666 666 665
1 777 777 776
1 888 888 887
1 999 999 998
14 444 444 313
15 555 555 414
16 666 666 515
17 777 777 616
18 888 888 717
19 999 999 818
Multiples of 9
1.
2.
3.
4.
5.
Same as the multiplier.
53 333 333 334
62 222 222 223
71 111 111 112
80 000 000 001
Magic Multiples
1.
2.
3.
4.
5.
6.
they are the same digits, rearranged.
No.
999 999.
999
99
One hundred and twenty four thousand five hundred and seventy eight.
Eight hundred and seventy five thousand four hundred and twenty one.
20
Maths Mysteries
Mysterious Primes
1. yes
2. yes
3. yes
4. yes
5. yes
6. 23
7. 31
8. 11
9. 19
10. 53
Amazing Number 2 520
1.
2.
3.
4.
5.
6.
1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
yes.
None of them. They all divide evenly into 2 520.
12, 14, 15, 18, 20, 21, 24.
yes.
8.
Pi (π)
1.
3.16049
2. yes
3. Circumference = 62.83 cm.
Some Fun With Pi (π)
The various responses will make for a light-hearted (but useful) sharing time which is sure to
leave at least some students with an impressive recall of π to many places.
21
Maths Mysteries
Zeno’s Famous Paradox
1.
2.
3.
4.
5.
1 second.
100/1000 = 0.1m=10cm.
0.1 X 0.1 = 0.01 seconds.
100/1000/100 = 0.001m = 1mm.
0.001/10 = 0.0001 seconds.
Palindromic Primes
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11
yes
no
no
yes
no
yes
no
no
yes
Magic Number 143
1.
143
143
143
143
143
143
143
143
143
X
X
X
X
X
X
X
X
X
1
2
3
4
5
6
7
8
9
Multiples of
143
143
286
429
572
715
858
1 001
1 144
1 287
X7
1
2
3
4
5
6
7
8
9
001
002
003
004
005
006
007
008
009
143
143
143
143
143
143
143
143
143
X
X
X
X
X
X
X
X
X
10
27
38
47
54
60
73
87
99
Multiples of
143
1 430
3 861
5 434
6 721
7 722
8 580
10 439
12 441
14 157
X7
10
27
38
47
54
60
73
87
99
010
027
038
047
054
060
073
087
099
2. Yes
3. No.
22
Maths Mysteries
Making 100 with 1-9
1)
2)
3)
4)
5)
6)
7)
8)
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
Note:


Putting a minus sign before the 1 gives one more solution: -1+2-3+4+5+6+78+9=100
Inserting a decimal point here and there gives: 1+2.3-4+5+6.7+89=100
Prime Fact
1st multiple of 6
2nd multiple of 6
3rd multiple of 6
4th multiple of 6
5th multiple of 6
6th multiple of 6
7th multiple of 6
8th multiple of 6
9th multiple of 6
10th multiple of 6
11th multiple of 6
12th multiple of 6
13th multiple of 6
14th multiple of 6
15th multiple of 6
16th multiple of 6
17th multiple of 6
18th multiple of 6
19th multiple of 6
20th multiple of 6




















6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
96
102
108
114
120
Prime
Numbers
5 and 7
11 and 13
17 and 19
23
29 and 31
37
41 and 43
47
53
59 and 61
67
71 and 73
79
83
89
97
101
107 and 109
113
119
23
Maths Mysteries
Mind-boggling Arrangements
1.
2.
3.
4.
120
720
39 916 800
Number of
cards
1
2
3
4
5
6
7
8
9
10
Number of
possible
arrangements
2X1
3X2
4X6
5 X 24
6 X 120
7 X 720
8 X 5 040
9 X 40 320
10 X 362 880
1
2
6
24
120
720
5 040
40 320
362 880
3 628 800
Puzzling Patterns
1.
2.
42 = 16
342 = 1156
3342 = 111556
33342 = 11115556
333342 = 1111155556
3333342 = 111111555556
33333342 = 11111115555556
333333342 = 1111111155555556
3333333342 = 111111111555555556
33333333342 = 11111111115555555556
3.
4.
7 X 9 = 63
77 X 99 = 7623
777 X 999 = 776223
7777 X 9999 = 77762223
77777 X 99999 = 7777622223
777777 X 999999 = 777776222223
7777777 X 9999999 = 77777762222223
5.
72 = 49
672 = 4489
6672 = 444889
66672 = 44448889
666672 = 4444488889
6666672 = 444444888889
66666672 = 44444448888889
666666672 = 4444444488888889
6666666672 = 444444444888888889
66666666672 = 44444444448888888889
16
6.
92 = 81
992 = 9801
9992 = 998001
99992 = 99980001
999992 = 9999800001
9999992 = 999998000001
99999992 = 99999980000001
4 156
24
Maths Mysteries
Happy Numbers
356
78 999
and
71 406 333
are happy numbers
Pervasive Palindromes
1.
6.
11.
16.
21.
55
2. 888
3. 404
4. 363
5. 1551
14641
7. 9339
8. 121
9. 121
10. 79497
9339
12. 7337
13. 1111
14. 4884
15. 7447
33033
17. 4774
18. 12221
19. 8998
20. 9339
No, 196 does not generate a palindrome.
Times Equals Plus
1.
3 + 1½
4 + 11/3
5 + 1¼
6 + 11/5
7 + 11/6
8 + 11/7
9 + 11/8
10 + 11/9
= 3 x 1½
= 4 x 11/3
= 5 x 1¼
= 6 x 11/5
= 7 x 11/6
= 8 x 11/7
= 9 x 11/8
=10 x11/9
= 4½
= 51/3
= 6¼
= 71/5
= 81/6
= 91/7
= 101/8
= 111/9
2.
996 + 11/995
997 + 11/996
998 + 11/997
999 + 11/998
1000 +11/999
3.
= 996 x 11/995
= 997 x 11/996
= 998 x 11/997
= 999 x 11/998
= 1000 x 11/999
= 9971/995
= 9981/996
= 9991/997
= 10001/998
= 10011/999
2 + 2 = 4 and 2 x 2 = 4
25
Maths Mysteries
Years in Reverse
a) 10:01 AM on January 10, 1001 is:
1001 1001 1001
c) 11:11 AM on November 11, 1111 is:
1111 1111 1111
e) 9:12 PM on December 21, 2112 is:
2112 2112 2112
26