Our mathematics teacher, Mr Chua Boon Woo introduced the usage of algebra with some magic tricks. Said he that a lot of tricks about numbers actually cling to algebra (and very, very, very tightly indeed!) and whatever numbers we picked will actually "fall down" to the one and only number.
This is one of the magic tricks he showed to us:
1. Pick either a 3- or 4-digit number.
2. Jumble the digits up.
3. Take away the smaller number from the larger number.
4. Circle any digit in your answer, any except 0(coz it's already a circle!!).
5. Tell the magician (whoever it is) the number left uncircled and he will tell you the number you have circled. You will find that he is always right.
Have you noticed something in the process that is awkward? It's the 0 thingy. Ever wondered why it asked you not to circle 0? It's reason that it is already a circle is only an excuse.
Here's the secret:
1. Take the 3-digit number as 100a+10b+c and the 4-digit number as 1000a+100b+10c+d.
2. Jumble the digits up. In this case, the 3-digit number is jumbled to a+10b+100c and the 4-digit-number as a+10b+100c+1000c.
3. This is where the "trick" comes in. Subtract the smaller number from from the larger number. In this case, the difference between the 3-digit-numbers is 99a-99c whereas 999a+90b-90c-999d for the 4-digit numbers. Notice that the answer you get will always be a multiple of 9.
4. Circle a random number except 0. Why? Remember that multiples of nine has digits that add up to multiples of 9? This is why once you circle a number leaving the others and tell the magician the other digits, the magician can subtract it from the nearest multiple of 9 which is greater. Circling 0 is not allowed as there will be two answers, 0 and 9 (as said, the reason of not circling 0 is that it is already a circle is just merely an excuse)!
This Is the Only Level
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