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Free Books Number Novelties Mathematical Novelties
Mathemagic • Combines the beauty of mathematical structure with the entertainment value of a trick
Choose a number between 1 and 63. Tell me if it appears on this chart.
Number Stomp • Using the numbers 1, 2, 4 and 8 Using the numbers 1, 2, 4 and 8 and addition, stomp to make all and addition, stomp to make all the numbers from 1 to 15. the numbers from 1 to 15.
Human Computer Stand side by side Each student represents a number Raise or lower hand to switch on/off
Tricky Table 9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10
Tricky Table 9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10
Tricky Table 9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10
Tricky Table 9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10
Tricky Table 9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10
Tricky Table • Add the four circled numbers. • 9 + 11 + 3 + 10 = 33 • Check your total against that of your neighbour
How to create a Tricky Table + 5 3 1 7 4 9 7 5 11 2 7 5 3 9 8 13 11 9 15 3 8 6 4 10
Finding the Magic Number • Add all the numbers on the outside of the table • 5 + 3 + 1 + 7 + 4 + 2 + 8 + 3 = 33
Create a Tricky Table +
Try a Multiplication Table x
Thrice Dice • Roll three dice • Stack on top of each other • Magician reveals the total • Add the numbers showing on the five faces that are touching.
Double Dice Instruction Dice Throw two dice (blue, red) Multiply the two top numbers 4 x 2 Multiply the two bottom numbers 3 x 5 Multiply the top of the blue die by 4 x 5 the bottom of red die Multiply the top of the red die by the 3 x 2 bottom of the blue die Add the four numbers
The answer 49
The algebra behind the trick • If we call the numbers on the top of each die a and b , then the numbers on the bottom of the dice will be 7 - a and 7 - b . • Consider the steps • Multiplying top numbers a x b = ab
Algebra cont • Multiplying bottom numbers (7 - a )(7 - b ) = 49 - 7 a - 7 b + ab • Multiplying top by bottom a (7 - b ) = 7 a - ab • Multiplying bottom by top b (7 - a ) = 7 b – ab • Combining the results • ( ab ) + (49 - 7 a - 7 b + ab ) + (7 a - ab ) + (7 b - ab ) • Simplified leaves 49.
Mobius Bands • You will need a strip of paper about as long and as wide as a ruler. • Give it a half twist and join • Cut lengthways • What happens?
Number Words • Choose a number (54) • Write it in words (fifty four) • Count the letters (9) • Write it in words (nine) • Count the letters …
Card Shark • Requires 26 cards • Split the 26 cards into a pile of 10 and a pile of 16 • Ask a friend to choose a card from the pile of 16 and place it on top of the pile of 10 to make eleven cards. • Place the remaining 15 cards on top of the eleven cards. • Deal to find the secret card
Card Shark Deal Once 26 cards are dealt face L R down, discard the 13 cards in the left pile. L R Collapse the right hand row, preserving the order of the L R cards. Continue until one card left
Crazy Calculator • Enter a three-digit number into a calculator (237) • multiply by 7 • multiply by 11 • multiply by 13 … • Start with a three-digit number, repeat and divide by 7, 11, 13.
Triple treat • Choose a two-digit number (39) • Repeat three times (393 939) • Divide by 13 • Divide by 21 • Divide by 37.
1089 Choose a three-digit number where the 461 hundreds digit is at least two more than the units digit. Reverse the digits 164 Subtract 461 – 164 = 297 Reverse the digits of the answer and then 792 + 297 = add this number to the answer Try another three-digit number and see what happens
1089 • Try • 1089 x 1 • 1089 x 2 • 1089 x 3 • 1089 x 4 …
1089 with algebra • The same pattern 900 + 180 + 9 is generated because of the initial restrictions of the puzzle. • We can represent this using some algebra • If a, b and c represent the digits in the original number we get 100a + 10b + c –(100c + 10b + a) = 99a – 99c or 99(a – c) • We know that a and c can only represent single-digit numbers and they cannot be equal because of the original restrictions.
1089 • The differences will be restricted to multiples of 99, that is 198, 297, 396, 495, 594, 693, 792 and 891 • When the numbers are reverse and added it leads to the following combinations 99 + 990, 198 + 891, 297 + 792 …
Think of a Number • Choose a number • 6 (a) • Double it • 12 (2a) • Add ten • 22 (2a + 10) • Treble it (3 x) • 66 (6a + 30) • Subtract 30 • 36 (6a) • Divide by six • #
Think of a Number II • Choose a number • 6 (a) • Add 20 • 26 (a + 20) • Double it • 52 (2a + 40) • Subtract 10 • 42 (2a + 30) • Halve it • 21 (a + 15) • Subtract the number • # you started with
Domino Trick • Ask your partner to choose a domino piece (without you seeing) • Multiply one of the numbers shown on the domino by 5 • Add 6 to the result • Double your answer • Add the number on the other half of the domino • Ask your partner to tell you his/her final number
Working out the original numbers • Subtract 12 to find the two numbers that were on the original domino • Could use two dice
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