Magical Age Cards

Tell the age of people (beween 0 and 63) from the cards they pick.

Some traditional  magic age cards  forgo the numbers 61, 62 and 63  (so that only 29 or 30 numbers per card are required, which are printed in a  5 by 6  pattern,  with or without a star in the 30th position).  Full-range cards  (with 32 numbers printed on each card)  are more satisfying.  Here are those 6 cards: 

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	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	08  09  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
04  05  06  07 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	02  03  06  07 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	01  03  05  07 09  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

Effect :   A spectator thinks of a number (up to 63) and tells you on what cards it is.
You call the exact number!

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Secret :   The  weight  of each card is the smallest number printed on it.  Any number is equal to the sum of the  weights  of the cards it appears on.  For example:

52   =   32 + 16 + 4

Magical Mind Reader - Multiples Of Nine

Pick a 2-digit number...

• Add the two digits together.
• Subtract that sum of digits from the original number.
• Look up the symbol corresponding to the result in a special table. 

How can the  magician  predict what that symbol is? The trick will become boring  (or obvious)  if the same table is used repeatedly.  Thus, a new table must be provided each time.  Several online implementation do this quite effectively, with nice graphics.  Examples:

 
 Magic Gopher  (British Council)

How fast can you discover the  secret  which makes this work?   [ Answer ] 

Answer :

The difference between a number and the sum of its digits
is always divisible by 9. The same symbol appears at all positions that are multiples of 9.

 

Mysterious Magical Trick - 1089

Pick a 3-digit number where the first and last digits differ by 2 or more...

• Consider the "reverse" number, obtained by reading it backwards.
• Subtract the smaller of these two numbers from the larger one.
• Add the result to its own reverse. 

 

Why is this always equal to 1089 ? 

 

This is one of the better tricks of its kind, because the effect of reversing the digits is not obvious to most people at first...  If the 3-digit number reads abc, it's equal to  100a+10b+c  and the second step gives the following result:

| (100a+10b+c) - (100c+10b+a) |     =     99 | a-c |

The quantity  | a-c |  is between 2 and 9, so the above is a 3-digit multiple of 99, namely: 198, 297, 396, 495, 594, 693, 792 or 891.  The middle digit is always 9, while the first and last digits of any such multiple add up to 9.  Thus, adding the thing and its reverse gives 909 plus twice 90, which is 1089, as advertised.