Monday , 27 February 2017
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Number Recreations – 1

[1] The sum of a square of three numbers in a calendar

Ask your friend to choose three successive dates from a calender. Let him do so in a column starting with the lowest number. You can tell the sum of 9 digits of the square so formed. How?

Ask your friend the least number he had thought of. Add 8 to it and multiply by 9. This will yield the desired sum.

[2] The age detector table

The table shown below helps you in guessing the age. What you have to do is to ask your friend about the columns where his age appears. Simply add up the numbers at the top of the columns indicated, and that sum will be equal to the age of your friend.

For example, your friend’s age is 23. This number as you can see is available in first, second, third and fifth columns. The top numbers in these four columns are 1, 2, 4, 16 – which add up to 23.

[I]
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
51
53
55
57
59
61
63

[II]
2
3
6
7
10
11
14
15
18
19
22
23
26
27
30
31
34
35
38
39
42
43
46
47
50
51
54
55
58
59
62
63

[III]
4
5
6
7
12
13
14
15
20
21
22
23
28
29
30
31
36
37
38
39
44
45
46
47
52
53
54
55
60
61
62
63

[IV]
8
9
10
11
12
13
14
15
24
25
26
27
28
29
30
31
40
41
42
43
44
45
46
47
56
57
58
59
60
61
62
63

[V]
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

[VI]
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

[3] Number of brothers and sisters one had – if both the parents were alive

Here is a simple trick by which you can tell the numbers of brothers and sisters one had.

[Step 1] : Add the number of parents (obviously it will be two in each case)

[Step 2] : Add to Step 1 the number of brothers and multiply the results by 2 and add one to it.

[Step 3] : Now the result of Step 2 is multiplied by 5 and the number of sisters is added to it.

[Step 4] : Subtract 25 from Step 3 to get the result.

[Step 5] : In the result of Step 4 the unit’s place indicates the number of sisters and the ten’s place the number of brothers.

Hence we can write the formula as : [(Parents + Brothers) x 2 + 1] x 5 + Sisters – 25

Example:

Suppose Krishna has 3 brothers and two sisters, then the solution would be:

[Step 1] : Number of Parents = 2

[Step 2] : (2 + 3) x 2+1 = 11

[Step 3] : 11 x 5 + 2 = 57

[Step 4] : 57 – 25 = 32

[Step 5] : Unit’s Place = 2 Sisters

Ten’s Place = 3 Brothers