A Lesson in the “Math + Fun!” Series
Dec. 2004 Math Crosswords Slide 1

About This Presentation
This presentation is part of the “Math + Fun!” series devised by Behrooz Parhami, Professor of Computer Engineering at
University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during the 2003-04 and 2004-05 school years. The slides can be used freely in teaching and in other educational settings.
Unauthorized uses are strictly prohibited. © Behrooz Parhami
Edition
First
Released Revised
Dec. 2004
Revised
Dec. 2004 Math Crosswords Slide 2

Start with a blank pattern
Number the squares
Fill squares with words
Backtrack if stuck
Design the clues
For example:
Across:
1. Not fresh
6. Residences
Down:
1. Smart
2. Sum
Dec. 2004 Math Crosswords
1 2 3 4 5
S T A L E
6
H
7
A
9
R
11
P
O
T
A
L
10
M E
?
8
A
S
O T
S
S
E
S
Slide 3

Standard: no isolated square, symmetric
Nonstandard: many single squares
(easy to design)
Math Crosswords
Fancy
Dec. 2004 Slide 4

http://www.pdos.lcs.mit.edu/cgi.bin/theme-cword
The MIT Web site listed at the top allows you to enter a few words into a blank pattern and then generates a crossword or replies that it could not do it.
For example, when
I entered the two highlighted entries,
I got this result
M
A
L
A
D
A
G
E
R
I
N
D
+ + W A N
+ S A L E
+ T I A R
+ + E F
S
A
+ T A
+ A V I
T
R
S
O
D
I
P
M
R
M
O
O
C
L A
+ T I
T I
T
O
U
N
S
S + O P S
+ + + O A R
+ C I
R A N
R C L
+
E
+ S E P I
+ +
A
T
+
E
R
A
+ G A E L
A
I
R
T
+ N I
I
+ +
C +
L
O
E
M
+
B
A
+
O
C
L
A
A
E
W
A
+ C O L
+ T U S H E S
R + + + I
+ M O T I
+ S
V
A
T
A
I
S
L
T I
L
+ S I
G M
+ + +
O
A
N
R
+
S
O
W
S
A
H
U
T
E
D
H
E
S
+ D A V I T
+ E R A S E
+ + A N A
+ T
+ C I
H E
S
A
T
+ + H O S E
Dec. 2004 Math Crosswords Slide 5

Words to use:
RECTANGLES
TRIANGLE
BAR GRAPH
HUNDRED
CIRCLE
ARC
ADD
SUB
TEN
SIX
S
U
C I
T
R
I
T
C L E
N
B A
R
R G R A
N
P H
R E C T A N G L E S
H U N
D
D R
L
E D
I
X
Dec. 2004 Math Crosswords Slide 6

http://www.puzzle-maker.com/CW/
1 T
2 S Q U A R E
I
A
3 A N
CIRCLE/Rim of a plate, usually
SQUARE/Shape of most tiles
ARC/Part of a circle
TRIANGLE/Three-sided shape
R
4 C I R C
G
L
E
E
Dec. 2004 Math Crosswords Slide 7

Activity 1: Making a Math Crossword
1 2
3 Across:
4
4. __________________________
6
5. __________________________ 5
8 9
7. __________________________
10. _________________________
7
10
Down:
1. __________________________
2. __________________________
3. __________________________
6. __________________________
8. __________________________
9. __________________________
S
U
B A
R
C I
R G R
T
R
I
C L E
P H
T
N
R E C T A N G L E S
I
H U N
D
D R
A
N
L
E D X
Dec. 2004 Math Crosswords Slide 8

Activity 2: Solving Some Other Types of Math “Crosswords”
So far, we have covered math crosswords that are just like regular crosswords but use math terms. Here are some other types.
Use digits 1 through 9 in the squares to make the result for each row or column equal to 10
Fill the circles with numbers so that the operations inside box arrows are valid
Fill in the missing letters so that each row and column has all the letters M A T H S
Dec. 2004 Math Crosswords Slide 9

Crossnumbers: “Crosswords” with Numbers
Across
1. 30 + 13
3. 52 + 32
6. 18 – 7
8. 69 – 20
10. 43 – 24
12. 47 – 26
14. 94 – 6
16. 79 – 47
19. 16 + 8
21. 52 – 29
23. 62 + 12
25. 4 + 21
27. 48 + 4
28. 13 – 3
Down
2. 78 – 47
4. 54 – 10
5. 50 – 9
7. 21 – 9
9. 45 + 45
11. 95 + 3
13. 23 – 10
15. 78 + 4
17. 50 – 28
18. 5 + 12
20. 51 – 9
22. 73 – 43
24. 30 + 15
26. 79 – 28
4 3
1 1
2 1
3 2
2 3
0
Dec. 2004 Math Crosswords Slide 10

Activity 3
Solve this crossnumber puzzle
Do the math next to the clues and enter numbers into the grid only after you have checked to see that the digits match
Dec. 2004 Math Crosswords Slide 11

Activity 4 9 8 9 2 4
Solve like an ordinary crossword puzzle.
Example for
1 across:
79,224
+ 19,700
98,924
Dec. 2004 Math Crosswords Slide 12

Across Down
1. 189 + 433 2. 633 / 3
4. 305 + 375 3. 13 + 7
7. 612 / 6 5. 719 + 168
10. 215 + 206 6. 627 + 214
12. 445 + 305 8. 291 – 90
14. 5 + 6
15. 570 / 5
9. 250 + 54
11. 27 + 185
17. 11 + 3 13. 405 + 11
18. 29 + 184 15. 9 + 4
20. 29 x 4 16. 425 – 15
23. 302 + 198 19. 193 – 90
25. 39 + 294 21. 201 – 97
27. 124 + 287 22. 35 + 296
29. 7 + 5 23. 375 + 126
30. 324 + 187 24. 305 x 2
32. 17 + 13 26. 15 + 306
33. 26 + 79 28. 156 – 26
34. 528 – 18 30. 12 + 43
31. 23 – 8
Dec. 2004
Activity 5
Math Crosswords
Solve this crossnumber puzzle
Slide 13

Activity 6: A Challenging
Crossnumbers Puzzle
Across
1. The cube of a whole number.
5. The number of square inches in a square yard.
6. The number of cubic inches in a cubic foot.
7. The number of millimeters in a meter.
Down
1. A number which is unchanged if the digits are reversed.
2. A prime number.
3. The number of feet in a mile.
4. The number of seconds in an hour.
+-----+-----+-----+-----+-----+-----+
|1 |
|
|
|
|
|2 |3 |OOOOO|4 |
|
|
|
|
|OOOOO|
|OOOOO|
|
|
+-----+-----+-----+-----+-----+-----+
|
|
|OOOOO|5
|OOOOO|
|
|
|
|
|
|
|
|
|
| |OOOOO| | | |
+-----+-----+-----+-----+-----+-----+
|6
|
|
|
|
|
|
|
|
|OOOOO|
|OOOOO|
|
|
| | | |OOOOO| |
+-----+-----+-----+-----+-----+-----+
|
|
|OOOOO|7
|OOOOO|
|
|
|
|
|
|
|
|
|
| |OOOOO| | | |
+-----+-----+-----+-----+-----+-----+
+-----+-----+-----+-----+-----+-----+
|1 | |2 |3 |OOOOO|4 |
| 3 | 3 | 7 | 5 |OOOOO| 3 |
| | | | |OOOOO| |
+-----+-----+-----+-----+-----+-----+
| |OOOOO|5 | | | |
| 1 |OOOOO| 1 | 2 | 9 | 6 |
| |OOOOO| | | | |
+-----+-----+-----+-----+-----+-----+
|6 | | | |OOOOO| |
| 1 | 7 | 2 | 8 |OOOOO| 0 |
| | | | |OOOOO| |
+-----+-----+-----+-----+-----+-----+
| |OOOOO|7 | | | |
| 3 |OOOOO| 1 | 0 | 0 | 0 |
| |OOOOO| | | | |
+-----+-----+-----+-----+-----+-----+
Dec. 2004 Math Crosswords Slide 14

Activity 7: Make a Crossnumbers Puzzle
Use no more than 7 black squares Use +,
-
, x, / in clues
Across: Down:
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
Dec. 2004 Math Crosswords Slide 15

Activity 8: Make a Crossnumbers Puzzle
Use no more than 7 black squares
Across: Down:
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
__________ __________
Use substitutions based on a = 3, b = 11, c = 8 (e.g., use 2b – c for 14)
Dec. 2004 Math Crosswords Slide 16

Cross-sums
Puzzle
Use only digits
1 to 9, each no more than once per puzzle entry.
Numbers above the diagonal show the sum of digits in spaces to the right.
Numbers under the diagonal show the sum of digits in spaces below.
Dec. 2004 Math Crosswords Slide 17

The product p and sum s for digits of each entry are given.
Across: Down:
# p s
1 18 10
# p s
1 4 5
3 32 12 2 48 14
4 40 13
6 7 8
8 10 7
3
5
125
15
7
0 9
35 12
9 30 10 8 6 5
Example: For 324, p = 24 and s = 9
1 2
3
6 7
9
4
8
5
Dec. 2004 Math Crosswords Slide 18

A Very Special Crossnumber Puzzle
All the clues in the following puzzle are the same, but no number is repeated in it.
Across and down clue: The square of a number.
1 2 3 4
5
6 7
Dec. 2004 Math Crosswords Slide 19

Thursday, January 6, 2005
Example to think about: Amy says that she was
10 years old the day before yesterday and that she will turn 13 next year. How is this possible?
Dec. 2004 Math Crosswords Slide 20