Chapter III: Number Games

Card Games

Card Location Tricks

Mathematical Card Trick. All this mathematics trick requires is an ordinary pack of cards. You don’t even need to do fancy shuffling.

Shuffle the cards thoroughly.
Deal out 36 cards and arrange them into a pile.
Ask your friend to pick a card, look at it and remember it, and then return it to the pile without letting you see it.
Shuffle the 36 cards.
Arrange the 36 cards into 6 rows of 6 cards each. Make sure to deal the top row from left to right. You should also deal the second row below it from left to right. Do the same procedure for each succeeding row underneath the one before.
Ask your friend which row the chosen card belongs to now. Remember the number of the row.
Then carefully pick up the cards in the same order you laid them down. This means that the first card on the left of the top row would be on top of the stack, and the last card on the right of the bottom row would be on the bottom of the stack.
Arrange the cards into 6 rows of 6 cards each; this time, however, spread the cards one column at a time. Proceed from one column to the next, instead of proceeding from one row to the next as performed earlier. Put down the first six cards in a column from top to bottom on the far left. Then just to the right of the first column of six cards, put down the next six cards in a second column of six cards. Repeat the process until you have 6 columns of 6 cards each. This looks the same as having 6 rows of 6 cards each – because it is actually the same.
Ask your friend once again which row the chosen card belongs to now.
When your friend tells you which row the chosen card is in, you can then identify the chosen card. How is this possible? If your friend tells you, for example, that the chosen card is in row 2 the first time, and in row 5 the second time around, then the chosen card is the one in the second column of the fifth row. The reason behind this is in the way you arranged the cards – what were rows the first time around became columns the second time around.

These card tricks that incorporate math strategies will surely impress your audience! If you want to find out more math magic using cards, subscribe and become a member of Math is Easy now.

Appearing Act Card Trick

Performing fun math tricks with your cards is very rewarding – especially when you see the surprised look on your audience’s faces! This mathematics trick is easy to learn and is nothing short of amazing.

Lay down 27 cards face up into a grid of 9 rows and 3 columns. Make sure to first deal out 3 cards horizontally in a row, and then 3 more cards just below the preceding row. Repeat this process until you have 9 rows. It is advisable to overlap cards in a column in such a way that the values of the cards are visible and the columns would not be so long. You can set aside the remaining cards. The 27 cards are all you need to perform the trick.

Let a spectator mentally choose a card and take note of it. Ask him or her which of the 3 columns the chosen card belongs to.

Gather the 27 cards into a deck.
Collect the cards vertically in such a way that the column containing the spectator’s chosen card is second.
Make sure to pick up the cards from the top of the column to the bottom, retaining their order. For example, if the spectator tells you that the chosen card is in column 1, then first gather either column 2 or 3, then column 1 (where the spectator’s chosen card is in), and then the remaining column.
Make sure that when you have gathered all cards, the top card of the deck is the top card of the column you collected first, followed by the rest of the column in order. The 10^th card of the deck should also be the card at the top of the column that contains the chosen card.
Gathering and keeping the cards in order will be easier for you if you overlap the cards as earlier suggested.

Deal the cards again following the same procedure as instructed earlier, which is to deal them horizontally across the rows first. Ask the spectator again which column the chosen card belongs to now.

Gather the columns vertically as instructed earlier. Make sure that the column containing the chosen card is collected second.

Deal out the cards again in the same manner as instructed above. Ask the spectator which column the chosen card belongs to this time and collect the cards in the same manner.

Tell the spectator that you know exactly what card he or she has picked. To make it more fun, add some drama into it. You can opt to deal out the cards face down. Don’t make your spectator notice that you are counting. You can also try not looking at the cards at all and just mentally do the counting. You can pretend to get a vibe or a hunch from certain cards, then hesitate, and then finally point out the right card. It’s going to be so much fun!

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Appearing Act Card Trick – Enhanced Version

In this card trick, you can make the card appear at any number position that a spectator chooses.

Deal 27 cards 3 times. For example, the spectator chooses the number 15, and then you perform the following:

The first time around, count in 3’s, that is to say, 1 2 3: 4 5 6: 7 8 9, and so on. Do this until you get to 15. As you can see, 15 is 3^rd of the 3 and is therefore put in 3^rd, that is, the bottom.
The second time around, count in groups of 3’s, that is to say, 1 2 3 counts as ‘1’, 4 5 6 counts as ‘2’ and 7 8 9 counts as ‘3’. Continue the count, this time, 10 11 12 counts as ’1’, 13 14 15 counts as ‘2’, and so on. Put the pile containing the spectator’s chosen card in second, that is, the middle.
The third time around, put the cards number 1 to 9 on top, 10 to 18 in the center, and 19 to 27 at the bottom. Put number 15, therefore, in the center again.

With the instructions above, you can make the chosen card show up at whatever number position the spectator has chosen.

Mathematics tricks such as this one will surely delight your audience. If you want to know other cool card tricks with underlying math strategies, subscribe and become a member of Math is Easy. By playing these games, you not only entertain yourself and your audience but you improve math skills as well!

Mind Games

Prediction Games

The Golden Prediction. This fun math trick may take some time, but the effect is surely amazing. Mathematics tricks like this one will make your audience think that you possess one of the coolest powers to have – the power of prediction.

Let’s start the math magic now, shall we?

Hand someone a piece of paper and a pencil and instruct him or her to:

On the piece of paper, number the first 25 lines (1, 2, 3, etc.)
On the first two lines, write down any two whole numbers.
Add the first two numbers and then write down the sum on the third line.
Add the last two numbers and then indicate the sum on the next line.
Continue the process of adding the last two numbers and writing the sum on the next line until he or she has reached 25 numbers on the list.
Choose any number among the last five numbers on the list. Divide the chosen number by the previous number or the number directly above it.

Now, prepare to amaze!

To build up the excitement and add some showmanship, remind your friend that you do not know what his or her original two numbers are. You have not seen any of the 25 numbers on the list and you absolutely have no clue which of the 25 numbers your friend has chosen right now.

This is your moment. Faking oodles of concentration and difficulty, slowly (and dramatically) come up with the number presently displayed on your friend’s calculator.

“Hmmm, it’s coming to me . . . Hold on, wait . . . I think I’m getting a one . . . Hmmm . . . and there’s this funny symbol – wait! Oh! It’s a decimal point . . . Then . . . I see it. I see it . . . It’s a six . . . And then a one again . . . Hmmm, then an eight, I believe . . . Wait, I see nothing . . . I lost it . . . Oh, it’s – it’s actually a zero! Yeah. Then, I see the number three? And another three . . . And then wait, what is that? Oh, it’s . . . It’s a nine! Did I get it?”

Yes, you got the answer right! If your subject chooses any number between the last five numbers on the list (#21 through #25) and divides it by the number directly above it, he or she will always come up with 1.618033989. This is actually the Golden Mean! (Granted your friend did the addition correctly the whole time, of course)

This is actually a wonderful bit of mathematical trivia. You start with any two whole numbers, create a Fibonacci-type addition list, get the ratio of two consecutive entries, and the ratio will lead to the Golden Mean! It becomes more accurate the further out you go. That is why we need 25 numbers to acquire sufficient accuracy. For this trick, the proof entails familiarity with the Fibonacci sequence, algebra and limits.

You want to know another fascinating fact. If you divide any of the last 5 numbers on your list by the next number instead of the previous number, the answer you get is the same decimal without the leading 1. The result is 0.618033989.

While delivering this mathematics trick, feel free to play with your imagination! You can find out more of these fascinating mathematics tricks right here! Subscribe and be a member of our website now. Discover the world of fun math.

Tricks to Impress Friends

Lightning Calculator. Here is a cool math trick that will surely wow your audience!

Ask your audience to write down their Social Security Number.
Then ask them to rewrite it so that the numbers are all scrambled up. (If they do not have a Social Security number, ask them to write down any 9 digits between 1 and 9.)
If there are any zeroes, instruct them to replace the zeroes with any other number between 1 and 9.
Then tell them to copy their nine numbers, in the same order, right next to the original nine numbers. They should have a number with 18 digits, with the first half the same as the second half.
Then tell them to change the second digit to a 7, and change the eleventh digit (this will be the same number as the second digit but belonging to the second half) to a 7 as well.

Here comes the magic. Bet your audience that you can tell them what is remaining after dividing the number by 7 faster than they could solve it by hand. The answer is zero. This is because 7 divides into this new number exactly with nothing left over!

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Math Trick – Age/Number. A simple trick with numbers yields an extraordinary result!

Think of your favorite number.
Multiply it by 25.
Subtract 35 from the result.
Then divide the current result by 5.
Add 7.
Multiply by 40.
Multiply your AGE by 2 then add this to your number.
Finally, divide your number by 2.
Look at your number. Lo and behold, the last 2 digits are your age and the first digit is your number!

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Cool Math Trick to Impress Friends. Grab a calculator and try out this neat trick. Input any three-digit number. For example, 729. Then repeat the digits to make it a 6-digit number. In the example, it is going to be 729,729. After that, divide it by 7, then by 11, then by 13. Now, how did you get that answer?

Yes, the number you have on the display right now is your original three-digit numbers. As explained by Edward H. Julius in “More Rapid Math Tricks and Tips,” repeating the three original digits is the same as multiplying by 1,000 (3 additional tens places to 729,000, in the example), then adding on the number again (729,000 + 729 = 729, 729).

That is also the same as multiplying by 1,001. Dividing by 7, 11 and 13 is actually the same as dividing by 7 x 11 x 13 or 1,001. Isn’t this an amazing trick with numbers? Whatever your original number was, you were, in effect, multiplying it by 1,001 and then dividing the result by 1,001, leaving you with your original three-digit number.

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Games to Sharpen Your Math Skills

The Three-Digit Reversal Technique

(1) Choose a three-digit number combination. Make sure the numbers do not repeat themselves.

e.g. 543

(2) Reverse the three-digit number.

e.g.        543 --> 345

(3) Then subtract using the greater number as the minuend and the other number as the subtrahend.

e.g. 543

   - 345

   -----

Note: The difference will always have a 9 in the middle and the other two numbers will add up to 9.

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The Secret Number Game

Can you guess the secret number?

The number is less than 100. It is more than 8 x 7 but less than 6x 10. The number is even. What is the number?

Easy? Now, try this one.

The number is less than 5 x 11 but is more than 3 x 12. The sum of all the digits in the number is equal to 6. It does not have a 3 or a 4 in it and it is not divisible by 4. The number is even. What is the number?

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Eleven Times

Here are quick steps to follow when multiply numbers by 11.

(1) Choose any two-digit number that you want to multiply by 11.

e.g. 45

(2) Separate the two digits.

e.g. 4_5

(3) Add the two digits.

e.g. 4 + 5 = 9

(4) Insert the sum in the space between the two digits.

e.g. 495

Now here is what you do when you have more than one digit to insert on the space in between.

e.g. 85 x 11

(a) Add the digits.

e.g. 8 + 5 = 13

(b) Insert the sum in the space between the two digits.

e.g. 8135

e.g. 8 + 1 = 9

(d) Insert the sum in the space before the remaining two digits.

e.g. 935

When multiplying three-digit numbers with 11, here is what you do:

e.g. 123

(1) Keep the first and last digit in position.

e.g. 1_3

(2) Add the last digit with the middle digit.

e.g. 3 + 2 = 5

(3) Insert the sum in the space before the last digit.

e.g. 1_53

(4) Add the first digit with the middle digit.

e.g. 1 + 2 = 3

(5) Insert the sum in the space after the first digit.

e.g. 1353

That’s it! You now have the easy-to-follow tricks to multiplying numbers by 11.

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Other Games and Techniques

Multiplication Tricks

20×20 Multiplication Techniques. These fun math tricks will teach you to multiply two-digit numbers from 11 to 19 in as quickly as five minutes without using any paper or a calculator.

Say, for example, 16 x 12.

(1) Place the greater number on top of the other.

e.g. 16

(2) Focus on the number on top and the second digit of the number below. Add them together.

e.g.  16 + 2 = 18

(3) Multiply the sum by 10, or simply add a zero after the last digit.

e.g. 18 x 10 = 180

(4) Multiply the second digit of the number below with the second digit of the number above it.

e.g. 6 x 2 = 12

(5) Add the products from steps 3 and 4.

e.g. 180 + 12 = 192

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Multiplying three-digit numbers and more with 11

(1) Write down the number to be multiplied with 11. Place a zero before the number.

e.g. 12345 x 11 --> 012345 x 11

(2) Follow the “Add the neighbor” technique, working your way from the second to the last digit up to the current first digit, which is zero. We retain the last digit because it has no neighbor.

e.g. 012345

     5 + 4 = 9

     3 + 4 = 7

     2 + 3 = 5

     1 + 2 = 3

     0 + 1 = 1

(3) Write the answers following their respective positions.

e.g. 135795

Learning math tricks such as this one will surely give you that edge. If you want to know more math strategies to improve math skills, subscribe to Math is Easy now.

Squaring Tricks

How to Calculate Square Roots. Do you want to get the square root of a number without using a calculator? If you are good with long division, you can try this quick method of finding pretty accurate square roots without using a calculator.

Let’s try for example, finding the square root of 24.6.

First, try making a guess. In this case, let us try 5 since is equal to 25, and that is pretty close to 24.6.
Divide 24.6 by 5. Hence, 24.6 / 5 = 4.92.
Make a new guess. This time, it should be between 5 and 4.92. Divide the result into 24.6 once more. Suppose our guess is 4.95. Hence, 24.6 / 4.95 = 4.96. This is pretty close to the actual square root of 24.6, which is 4.9598.
You can do Steps 2 and 3 again in order to attain the level of accuracy that you want.

This trick works because n x n = 24.6 and n = 24.6 / n. Thus, the actual square root should always be somewhere between 24.6 / n and n.

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Click here to go to Chapter IV: Doing Math in the Real World!

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