Appear to Read Someone's Mind with Numbers

The simple rules of numbers create many surprising effects. Here are three math tricks that take advantage of this so you can show off to friends. Read through the trick first so you can find one that matches your friends' math skills.

Steps

Predicting a Number (Easy)

  1. Ask your friend to pick a number. He should keep this number secret from you. Tell him not to forget, since he'll have to remember it later.
    • We'll go through an example where your friend picks the number 6.
    • Even kids can do the math in this trick, as long as they can multiply and divide by 2. A young kid might need to whisper the number to another person, so she can remind him later.
  2. Have your friend double the number. Say "Now double the number you chose, but don't tell me the answer."
    • In our example, 6 x 2 = 12.
  3. Show him 10 fingers. Ask him to add 10 to his last answer.
    • 12 + 10 = 22.
  4. Divide the answer by 2. Tell your friend you're trying to read his mind, but the number is too big right now. Ask him to divide the answer by 2 to make it smaller.
    • 22 ÷ 2 = 11.
  5. Subtract the original number. Ask him to take the last answer and subtract the original number he picked.
    • The person in our example picked 6, so he would calculate 11 - 6 = 5.
  6. Announce that the answer is 5. No matter what number your friend chose, he will end up with 5 as his final answer. Announce that you have read his mind, and the last number your friend wrote down is 5. If there are other people in the room, have your friend show them the piece of paper to prove it.
  7. Know why this works. Most of these steps are there just to make it hard for people to follow the problem. After you double the chosen number, divide it by two, and subtract the number, you've cancelled out the original number completely. Now it doesn't matter what your friend chose. The answer only depends on the extra numbers and instructions you gave him, which happen to lead to 5 in this trick.

The 37 Trick (Intermediate)

  1. Have someone write down the same digit 3 times. She should keep the paper hidden from you at all times. A calculator will come in handy for this trick.
    • For example, she could write down 555.
  2. Instruct her to add all three digits together. Ask the subject of the "mind reading" to separate the three digits and add them together.
    • In this example, 5 + 5 + 5 = 15.
  3. Divide the larger number by the smaller one. Confirm that the subject now has two numbers written down, a three-digit number and a smaller one. Ask her to take the three digit number and divide it by the smaller one.
    • 555 ÷ 15 = 37.
  4. Announce that she's thinking of the number 37. Whether she chose 111, or 999, or one of the options in between, your volunteer will always end up with 37 as her answer!
  5. Learn why this works. There's no deep trick here; these are just properties of the numbers involved. 37 x 3 = 111. Each "jump" up (111 → 222 → 333, etc.) adds another 111, so you're adding 37 multiplied by three each time. Looking at the sum of the digits (1+1+1 → 2+2+2 → 3 + 3 + 3, etc.), you also happen to be adding three each time. By putting this in a division problem, each jump up means dividing by another three each time. These two effects cancel each other out and you get back to 37.

Guessing The Secret Digit (Advanced)

  1. Hand a calculator, pencil, and paper to a volunteer. This trick involves large numbers, so a calculator that has plenty of space will come in handy. Tell him that you'll be reading his mind, so he should keep everything on the paper and calculator hidden from you.
    • This trick also requires some quick thinking on your part. It's nothing harder than addition, but you'll need to be fast and error-free.
  2. Instruct a volunteer to write down three positive, consecutive numbers. These can be any whole numbers, but they must be consecutive. (There can be no whole numbers between them.)
    • For example, your volunteer could pick 19, 20, and 21.
    • If the calculator only has room to display eight digits, the numbers must all be between 1 and 21. If it only has room to display six digits, make it 1 to 9.
  3. Ask him to multiply the three numbers together. After he finds the answer on the calculator, have him write it down on the piece of paper.
    • In our example, 19 x 20 x 21 = 7980.
  4. Tell the volunteer to repeat this for three other consecutive numbers. Next, the person you're "mind reading" secretly picks three more consecutive numbers. He multiplies them together and writes them down next to his first answer.
    • Let's say he picks 12, 13, 14. He multiplies 12 x 13 x 14 = 2184.
  5. Have him multiply the two products together. Now the volunteer multiplies his two answers together and writes down the result.
    • 7980 x 2184 = 17428320.
  6. Tell the volunteer to shuffle all but one digit. Explain that you only have enough power to read one of the digits from his mind. Ask him to pick one secret digit in the number, then write down the other digits after shuffling them in any order.
    • For example, if he picks 4 as the secret digit, he could shuffle the rest of the digits as 2287013.
  7. Add the shuffled digits as he reads them aloud. Remind him that he must keep one digit secret. Have him read the other digits slowly and clearly while you add them in your head.
    • For example, he would read "2... 2... 8... 7... 0... 1... 3." You add these together as he goes, getting a total of 23.
  8. Find the secret digit. All of the digits in his answer, including the secret one, will add up to a multiple of 9. Once you know this, there are two ways to find the secret digit. Here they are, using our example:
    • The non-secret digits add up to 23, and you know the next multiple of 9 is 27. Think 27 - 23 = 4, so the last digit must be 4.
    • If you're not sure what the next multiple of 9 is, add the digits in your sum and repeat. For example, 23 → 2 + 3 = 5. Now the next multiple of 9 is 9, and 9 - 5 = 4.
  9. Know what to do if the shuffled digits add up to 9. If you add the digits he spoke out loud and you already have a multiple of 9, there are two possibilities. Either the secret digit is 0, or the secret digit is 9. Make a guess at one of them. If you get it wrong, make a joke ("I knew I should have studied harder in telepathy school"), then guess again with the second possibility.
  10. Understand why this works. Any three consecutive numbers includes a multiple of 3, so the product of the trio will also be a multiple of 3. Since you repeat this and multiply the two answers together, you are finding the product of two multiples of three. This product is always a multiple of 9 (since 3 x 3 = 9). All multiples of 9 have the property described above, where all of their digits sum to another multiple of 9.

Tips

  • There are many more math tricks out there. If you Learn-Algebra or already know it, you can come up with your own variations on the number prediction trick. (Hint: write the number your friend guesses as x, and come up with calculations that cancel out the x.)

Warnings

  • Don't repeat the same trick a second time in front of the same person.

Things You'll Need

  • Paper and pencil
  • A calculator (recommended)

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Sources and Citations

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