Saturday, September 30, 2000
M I N D  G A M E S


Tricks of the trade

"Pick three different numbers between 1 and 9. Write the numbers next to each other, largest first and smallest last, to form a single three-digit number. Do not to reveal it to me," says the magician to a little kid. The kid, who is too wise for a child of his age, obeys.

"Now, form a new three-digit number by reversing the digits, putting the smallest first and the largest last. Write the new number below the first number. Subtract the lower (smaller) of the two from the upper (larger). You may not tell me the result," the magician says.

"Add up the three digits of the number that results from subtracting the smaller from the larger of the two. Did you do it?" the magician says. "Yes," the kid replies. "Is the sum 18!" the boastful magician asks again. "Yes," the kid replies.

Magician: "If you tell me what the first or last digit of the answer is, I will tell you what the other two digits are."

 


The magician does not tell the kid that this is possible because the middle digit is always 9, and the other two digits always add up to 9. To get the digit other than the middle one (which is 9) and other than the digit that the kid will tell the magician, subtract the digit the kid will tell the magician from 9.

As expected, the magician gives the answer and mesmerises the audience. The kid also knows what the magician has done, but keeps quiet. He interrupts the magician when he is savouring the applause.

Reverse gear
123456789
x 8 + 9
=987654321

The kid to the magician: "Write down any nine-digit number using digits between 1 and 9 and jumble it up. If you choose to write a number with zeroes in it, change these to any other number between 1 and 9. Then copy the new nine digits in the same order, right next to the orginal nine numbers. Have you now got 18 digits, with the first half the same as the second half?"

Magician: "Yes...uh...but..."

The kid: "Now, change the second digit to a 7 and the eleventh digit (same number as the second digit, but in the second set of nine digits) to a 7 also. Divide the number by 7. I can tell you what is left." "Tell me," says the magician.

"Zero, nothing, abracadabra and your number has vanished," says the kid. The kid does not tell him that 7 divides into this new number exactly with nothing left over, always. Kid: "If you wish to impress the audience again with your psychic powers, I can show you another trick. Attention please." Magician: "Excuse me, but isn’t it my show?"

Kid: "Yes, but your trick was too obvious and boring. Let me show them a new thing. Number every person in the group, beginning from 1."

The magician does it. Kid: "Get a ring and tell someone in the audience to wear it. Let them do it while I leave the room." After returning, the kid says, "I can tell not only who has the ring, but also in which hand and which finger it is on. However, you will have to do some easy mathematics for me and tell me the answers."

Kid: "Multiply the number of the person with the ring by 2. Add 3. Multiply the result by 5. If the ring is on the right hand, add 8. If the ring is on the left hand, add 9. Multiply by 10. Add the number of the finger (the thumb = 1, and so on). Add 2. Tell me the answer."

Someone in the audience tells him the answer. The kid, then, mentally subtracts 222 from it, and gives them the answer, beginning with the right-hand digit of the answer.

Magician: "How did you do it?"

Kid: "Everyone, but I, knew that the ring was on the third finger of the left hand of person number 6. Multiply 6 by 2, you get 12. Add 3 to it to get 15. Multiply it by 5 to get 75. Since the ring was on the left hand, everyone added 9 to it to get 84. Multiply this by 10 and we get 840. Add the number of the finger (3) to get 843. Add 2 to it and get 845. I mentally subtracted 222 from it to get 623. The right-hand digit (3) told me that the ring was on the third finger. The middle digit told me that it was on the left hand (the right hand = 1). The left-hand digit told me it was person 6 who was wearing the ring. If the number of the person is over 9, you will get a four-digit number, and the two left-hand digits will be the number of the person with the ring."

Magician: "I don’t know if this is magic or what." Kid: "Tricks of the trade, Sir."

— Aditya Rishi