Friday, August 03, 2007
Again the missing number
This trick is a bit more difficult then number 1 above, but once you discover 'the secret' and once you have practised this trick a few times (perhaps using pen and paper to begin with) you'll find it quite easy!
(a) Ask someone to write on a piece of paper (so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Ask them to add up all the digits of the number and tell you the result. Now, you don't need to remember this result, just continue adding the digits of the number that they tell you until you get a single digit 1 to 9 only. e.g. for 29, 2+9=11, 1+1=2, just remember 2! Call this number N.
(c) Then tell them (trying to seem like you are making these numbers up as you go) to add 6543 and write down the result. Then subtract 567 and write down this result. You can also continue and ask them to add or subtract other numbers like 432. Once you discover the 'secret' of this trick you'll see that many other numbers can be 'safely' added or subtracted and the trick still works!
(d) Now, as an option, you can let them choose which of the above results they wish to use. But whatever, ask them to add up the digits of the number and satisfy themselves that it is not the same as before!
(e) Ask them to circle any digit in the number selected except zero.
(f) They can then read out (slowly), all the other digits in random order. And you will tell them what the digit is that they circled.
(g) To find the missing digit, simply add up all the digits that they give you - repeatedly - until a single digit 1 to 9 is obtained. If this value is the same as the number N (see b. above), then the number they circled was 9. Otherwise, subtract this value from N. If this result is positive this is the number they circled! If negative, add 9 to the value and this is the number circled! e.g. If the digits are 9, 8, 8, and 4 then 9+8+8+4=29, 2+9=11, 1+1=2, If N=5, then 5-2=3 Therefore the number circled was 3. If N=1, then 1-2=-1, -1+9=8, the number circled was 8.
How does this trick work?
This trick works for the same reason that the first 'missing number trick' works - ‘digital roots’.
(a) Ask someone to write on a piece of paper (so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Ask them to add up all the digits of the number and tell you the result. Now, you don't need to remember this result, just continue adding the digits of the number that they tell you until you get a single digit 1 to 9 only. e.g. for 29, 2+9=11, 1+1=2, just remember 2! Call this number N.
(c) Then tell them (trying to seem like you are making these numbers up as you go) to add 6543 and write down the result. Then subtract 567 and write down this result. You can also continue and ask them to add or subtract other numbers like 432. Once you discover the 'secret' of this trick you'll see that many other numbers can be 'safely' added or subtracted and the trick still works!
(d) Now, as an option, you can let them choose which of the above results they wish to use. But whatever, ask them to add up the digits of the number and satisfy themselves that it is not the same as before!
(e) Ask them to circle any digit in the number selected except zero.
(f) They can then read out (slowly), all the other digits in random order. And you will tell them what the digit is that they circled.
(g) To find the missing digit, simply add up all the digits that they give you - repeatedly - until a single digit 1 to 9 is obtained. If this value is the same as the number N (see b. above), then the number they circled was 9. Otherwise, subtract this value from N. If this result is positive this is the number they circled! If negative, add 9 to the value and this is the number circled! e.g. If the digits are 9, 8, 8, and 4 then 9+8+8+4=29, 2+9=11, 1+1=2, If N=5, then 5-2=3 Therefore the number circled was 3. If N=1, then 1-2=-1, -1+9=8, the number circled was 8.
How does this trick work?
This trick works for the same reason that the first 'missing number trick' works - ‘digital roots’.
// posted by Kritidas @ 2:46 AM 
