Mathemagic 2015
Mary Jane Sterling
Session 1 (see missing digits for extras)
Think of a number
Basic trick
Show algebra
Create own trick
January 1st for any year in 21st century
Moebius strip (adding machine tape; scotch tape)
Session 2
Quick computing
Squaring numbers ending in 5
Finding next perfect square
Multiplying by 11
Russian Peasant Multiplication
Mind-reading cards (5 index cards)
Regifting Robin
Session 3
Casting Out Nines
Train cars
Sherlock Holmes
Session 4
Chocolate math
Adding trick with 3-digit number
Prediction
Flexagons (adding machine tape, glue, scissors)
Extras
Think of a number – missing digits
Magic Squares
3 by 3
4 by 4
Handout
Drawing circles, ovals
Day of the week for any date
Vanishing Act
Domino Feat
Calendar Sum
Think of a number
1) Think of a one-digit number.
2) Multiply it by 9.
3) Add the digits of your answer together.
4) Subtract 5.
5) If A = 1, B = 2, C = 3, etc. determine what letter is represented by the answer.
6) Think of a country beginning with that letter.
7) Think of a mammal beginning with the second letter of that country.
8) What is the color of that animal?
There aren’t many grey elephants in Denmark, are there?
96% will choose Denmark (Djibouti, Dominica, Dominican Republic)
85% will choose elephant if don’t limit to “mammal” (eel, eagle, elk)
Think of a number (answer will be 2)
1) Think of a number.
2) Multiply it by 3.
3) Add 6 to the result.
4) Divide the answer by 3.
5) Subtract the original number.
Your answer is 2.
Think of a number (answer will be 5)
1) Think of any three-digit number.
2) Add 7 to it.
3) Multiply the result by 2.
4) Subtract 4 from that result.
5) Divide the difference by 2.
6) Subtract the original number from this result.
Your answer is 5.
January 1st for any year in the 21st century
1) First memorize the following:
Mon Tues Wed Thurs Fri
Sat
Sun
1
2
3
4
5
6
7 or 0
2) Pick a year. Consider just the last two digits.
3) Find 25% of the year; discard any decimals.
4) Add the result to the original two digits.
5) Subtract the largest multiple of 7 from the sum.
6) The difference corresponds to the day of the week.
Exception:
If the year is a leap year, decrease the amount determined in step 3 by 1.
http://www.searchforancestors.com/utility/perpetualcalendar.html
Moebius Strip
Cut a 2-foot piece of adding machine tape. Tape together the ends after making a “twist”.
1) Cut it in half down the center. Result?
2) Create another strip and cut it in thirds. Result?
3) Create another strip, but give it two twists and then cut it down the center. Result?
Quick Computing
1) Squaring numbers ending in 5
You first write down the last digits of the answer: 25. Then take the digit or digits in front of the original 5 and
multiply them by the next bigger number. Put that product in front of the 25, and you have the square of the
number you want.
2) Finding the next perfect square
Take the square of the number you already have and add the root plus the next number (the root of the square
you want).
3) Multiplying by 11
When multiplying a number times 11, you just have to add up adjacent digits. Put 0’s in front of and behind the
number. Add up each pair of adjacent digits starting at the far right. If one or more of the sums is greater than
9, then you carry the tens digit over to the sum to the left.
Russian Peasant Multiplication
You might call Russian Peasant Multiplication nothing more than multiplication avoidance. It’s an interesting
method, but multiplying the conventional way is usually quicker. Here are the rules to using Russian Peasant
Multiplication:
1) Write the two numbers you’re multiplying at the top of two columns.
2) Double the number in the first column and halve the number in the second column – write the results
under their respective starting numbers. If the number in the second column is odd, just drop the remainder.
3) Look at the numbers that were doubled and halved; if the number in the second column was even,
then cross out that entire row.
4) Keep doubling and halving until the number in the second column is a 1.
5) Add up the remaining numbers (the ones not crossed out) in the first column. The total of those
numbers is the product of the original numbers.
For example, multiplying 23 × 49, write the numbers at the top of two columns.
23
49
46
24
Double the 23; halve the 49 and drop the remainder.
92
12
Double the 46; halve the 24.
Since 24 is even, cross out the entire row above.
184
6
Double the 92; halve the 12.
Since the 12 is even, cross out the entire row above.
368
3
Double the 184; halve the 6.
Since the 6 is even, cross out the entire row above.
736
1
Double the 368; halve the 3 and drop the remainder.
You have a 1 in the second column; stop.
Add up the numbers in the first column: 23 + 368 + 736 = 1127. That’s the product of 23 × 49.
Mind-Reading Cards
Re-Gifting Robin
1) Pick any two-digit number.
2) Subtract both the first and second digits from your number.
3) Find the color corresponding to your result in the chart.
Your color is Silver.
1
Orange
12
Teal
23
Aqua
34
White
45
Silver
56
Black
67
Red
78
Orange
89
Blue
2
Red
13
Green
24
Yellow
35
Orange
46
Blue
57
Silver
68
Green
79
Mauve
90
Silver
3
Blue
14
Violet
25
Amber
36
Silver
47
Pink
58
Coral
69
Copper
80
Red
91
Cyan
4
Green
15
Ivory
26
Lilac
37
Jade
48
Yellow
59
Sepia
70
Navy
81
Silver
92
Peach
5
Yellow
16
Blue
27
Silver
38
Olive
49
Black
60
Ochre
71
Lemon
82
Tan
93
Yellow
6
Purple
17
Beige
28
Indigo
39
Puce
50
Purple
61
Plum
72
Silver
83
Yellow
94
Pink
7
Teal
18
Silver
29
Rose
40
Red
51
Orange
62
Yellow
73
Green
84
Blue
95
Plum
8
Orange
19
Sepia
30
Copper
41
Ivory
52
Melon
63
Silver
74
Grey
85
Tan
96
Amber
9
Silver
20
Purple
31
Beige
42
Ochre
53
Copper
64
Pink
75
Cyan
86
Lilac
97
Green
10
Gold
21
Rose
32
Yellow
43
Green
54
Silver
65
Gold
76
Coral
87
Navy
98
Yellow
11
Black
22
Lilac
33
Red
44
Grey
55
Ecru
66
Cherry
77
Puce
88
Lime
99
Silver
Casting out 9’s
1492
1984
2006
1776
1812
9070
Here’s how to use Casting Out Nines in a multiplication problem. You cross out nines or sums of nines in the
first number – just the digits in that first line. If you can’t cross out any, just add up the digits. If the sum is
bigger than nine, add up those digits. Do the same thing with the second number. Then do the same thing with
the answer. Here’s an example.
4812
7535
36, 258, 420
Train Cars
Bar
Diner
Shower
Engine
Caboose Mail
Start in Shower, Diner, Club or Mail
Move 4
(takes away Staff)
Move 5
(takes away Club)
Move 2
(takes away Mail)
Move 3
(takes away Baggage and
Caboose)
Move 3
(takes away Shower)
Move 1
(you’re in Diner)
Bag
Club
Staff Car
Train Cars
(David Copperfield)
Put up Shower, Diner, Club, Mail
Have to move horizontal or vertical
Why:
First move, always end up in one of starting (middle
squares of sides)
Second move, always end up in corner or center
Third move, always end up in corner or center
Fourth move, always end up in middle of side
Fifth move, always end up
Sixth move, always end up in Bar or Engine
Sherlock Holmes
1) The Murderer stands in the Hall. Sherlock Holmes is blindfolded and cannot see where the Murderer is
going.
2) Someone throws a die, and states the number out loud. The Murderer walks through as many doors on the
plan of the house as the number called out.
3) Sherlock says, “I know that the Murderer is not in the ________, so take away the __________.
4) The process is repeated until Sherlock can say, “I know that the Murderer is in the ____________. You are
under arrest.”
Process:
If the Murderer starts in the Hall, four rooms are one door away. These are “odd” rooms. the other rooms are
two doors away; they are “even” rooms.
Using the principles of: odd + odd = even, odd + even = odd, and even + even = even, Sherlock keeps track of
the rooms the Murderer can’t be in. Sherlock must reserve the right not to remove a room in certain cases.
Chocolate Math (The numbers in step 5 correspond to 2015.)
1) Write down the number of times you each chocolate in one week.
2) Multiply that number by 2.
3) Add 5 to the result.
4) Multiply that answer by 50.
5) If you’ve already had your birthday this year, add 1765; if you have not had your birthday this year, add
1764.
6) Subtract the year you were born from the total. Look at your answer.
The last two digits are your age, and the digits before your age are the number of times you eat chocolate each
week.
Adding trick with three-digit number
1) Have someone write down three, three-digit numbers in a column to be added.
2) You add two more three-digit numbers and then “quickly” write the sum of the five numbers at the bottom.
To choose the fourth and fifth numbers:
Fourth number and first number add up to 999.
Fifth number and second number add up to 999.
The answer will be 2000 plus the third number minus 2.
Prediction
(Preparation: write the number 1089 on a piece of paper; fold it and label it “prediction”.)
1) Pick a three-digit number – all three digits different.
2) Reverse the digits and subtract the smaller number from the larger number. If the result is 99, add a zero to
the front to make it 099. (Tell them: if the result is two digits, put a 0 in front to make it 3 digits.)
3) Add the reverse of that number to the result.
4) Open up your prediction.
Flexagons
G
1
3
2
1
2
1
3
2
3
2
1
3
1
3
2
1
2
G
3
Using number from Prediction
(This works best if someone has a calculator.)
1) Think of a three-digit number; multiply it by 1089.
2) Ask how many digits there are in the answer. (Answer will be six.)
3) Call out any five of the six digits in any order. (Will promise to figure out which digit is missing.)
The product has to be a multiple of 9. So add up the five digits given and figure out what has to be added to
make the sum of the digits a multiple of 9. If the sum ends up being a multiple of 9, then the missing digit is a 0
or 9. Can say, “You didn’t leave out a 0, did you?” If response is no, then missing digit is 9.
Magic Squares
7 12 1 14
2 13 8 11
16 3 10 5
9 6 15 4
Day of the Week
Find the day of the week for any day, any year.
1) Select a date: Month, Day, Year
2) Let d = day
3) Let m = month (except for January and February; they become months 13 and 14 of the previous year)
4) Let y = year (except for January and February dates – they are the previous year)
5) Compute the following. The brackets indicate dropping remainders (greatest integer function).
 3(m  1) 
 y  y   y 
N  d  2m  
 y 

2

 5 
 4  100   400 
6) Now divide N by 7. The remainder tells you the day of the week using:
1
2
3
4
5
6
0
Sun Mon Tues Wed Thurs Fri
Sat
http://www.searchforancestors.com/utility/perpetualcalendar.html
Domino Feat
Choose any domino.
Multiply one of the numbers by 5. Add 8. Multiply by 2. Add the other number on the domino. Ask for the
answer.
(Subtract 16 from the answer. The two digits in the answer are the two numbers on the domino.)
Calendar Sum
Select any square arrangement of dates on a calendar (3 rows, 3 columns). Ask for the lowest number in the
square. The sum of the nine numbers is 9(8 + lowest number).
Vanishing Act
16
6
6
10
14
10
6
12
10
8
6
4
2
5
10
15
20
25
30
14
Appears to go from 16 X 16 = 256 to 10 X 26 = 260. The diagonal in the rectangle isn’t really a straight line.
111.78 + 69.43 = 181.21
12
10
A
8
6
D
111.78
69.43
4
B
2
C
5
10
15
20
25
30
This was sent to me by Sanford Gordon, one of the class participants.
Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.
Cheryl gives them a list of 10 possibilities: May 15, May 16, May 19, June 17, June 18, July 14, July 16,
August 14, August 15, August 17.
Cheryl whispers to Albert the month of her birthday and whispers to Bernard the day.
Albert says: I don’t know when your birthday is, but I know Bernard doesn’t know, either.
Bernard say: I didn’t know originally, but I do now.
Then Albert says: Well, now I know, too!
Do you know Cheryl’s birthday? Here’s the solution, in case you haven’t figured it out.
It helps to put the list of 10 dates into table form:
Now let’s examine what Albert and Bernard say. Albert goes first:
I don’t know when your birthday is, but I know Bernard doesn’t know, either.
The first half of the sentence is obvious — Albert only knows the month, but not the day — but the
second half is the first critical clue.
The initial reaction is, how could Bernard know? Cheryl only whispered the day, so how could he have
more information than Albert? But if Cheryl had whispered “19,” then Bernard would indeed know
the exact date — May 19 — because there is only one date with 19 in it. Similarly, if Cheryl had told
Bernard, “18,” then Bernard would know Cheryl’s birthday was June 18.
Thus, for this statement by Albert to be true means that Cheryl did not say to Albert, “May” or “June.”
(Again, for logic puzzles, the possibility that Albert is lying or confused is off the table.) Then Bernard
replies:
I didn’t know originally, but now I do.
So from Albert’s statement, Bernard now also knows that Cheryl’s birthday is not in May or June,
eliminating half of the possibilities, leaving July 14, July 16, Aug. 14, Aug. 15 and Aug. 17. But Bernard
now knows. If Cheryl had told him “14,” he would not know, because there would still be two
possibilities: July 14 and Aug. 14. Thus we know the day is not the 14th.
Now there are only three possibilities left: July 16, Aug. 15 and Aug. 17. Albert again:
Well, now I know too!
The same logical process again: For Albert to know, the month has to be July, because if Cheryl had
told him, “August,” then he would still have two possibilities: Aug. 15 and Aug. 17.
The answer is July 16.