Showing posts with label mathematical puzzles. Show all posts
Friday, February 27, 2015
Snake
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7:30 AM
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How are we to seat them within our only 8 remaining spaces?"
frowned the manager of the theatre. Everyone was well aware of the
problems of these eight people. They came as a group, but each person
loathed one or two of the other people and could not stand to be near
them.
The assistant manager gestured to the plan of seats remaining. "I have made eight counters to represent each of the people in this group. I have numbered them logically. Person 1 and 8 only hate 2 and 7 respectively. All the others hate the numbers on either side of them." He rubbed his chin in thought, "the only problem is how can we arrange them so that noone is right next to anyone they hate?"
Place the counters 1 to 8 in the grey squares above such that no two consecutive counters are adjacent to one another horizontally, vertically nor diagonally.
The assistant manager gestured to the plan of seats remaining. "I have made eight counters to represent each of the people in this group. I have numbered them logically. Person 1 and 8 only hate 2 and 7 respectively. All the others hate the numbers on either side of them." He rubbed his chin in thought, "the only problem is how can we arrange them so that noone is right next to anyone they hate?"
Place the counters 1 to 8 in the grey squares above such that no two consecutive counters are adjacent to one another horizontally, vertically nor diagonally.
Snake Puzzle Solution
Counters 1 and 8 need to be in the middle since they each have only one number that they cannot be neighbours with. Hence 7 and 2 must go in the sidewings, and the rest is trivial.3  5  
7  1  8  2 
4  6 
Saturday, February 7, 2015
Southern Cross
Games Reviewer
7:08 AM
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There is a missing number in the table below.
What number goes in the blank box?
4  5  6  7  8  9 

61  52  63  94  46 
What number goes in the blank box?
Southern Cross Puzzle Solution
The missing number is 18. The numbers in the bottom row are the square of the numbers in the top row, but with their digits reversed.4  5  6  7  8  9 

61  52  63  94  46  18 
Wednesday, January 28, 2015
Canopus
Games Reviewer
7:03 AM
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There is a number made of eleven tens of thousands, eleven thousands, eleven hundreds, and eleven units?
What is that number?
What is that number?
Canopus Puzzle Solution
A nice and simple sum does the trick.…110,000  + 
11,000  + 
1,100  + 
11  = 
__________


122,111 
Monday, December 29, 2014
100
Games Reviewer
6:44 AM
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Find at least four ways of writing the number 100, each time using only one digit repeated five times.
For example: (999 / 9)  9 = 102 (but you must get 100, not 102!!!)
Good luck!
For example: (999 / 9)  9 = 102 (but you must get 100, not 102!!!)
Good luck!
100 Puzzle Solution
 111  11 = 100
 (3 * 33) + (3 / 3) = 100
 (5 * 5 * 5)  (5 * 5) = 100
 (5 + 5 + 5 + 5) * 5 = 100
 (11  1) ^ ( 1 + 1) = 100 [Thanks to Steven Renich for that one!]
 ((2 * 2 * 2) + 2) ^ 2 = 100 [Thanks to David Cohen for this other one!]
 ((99 * 9) + 9) / 9 = 100 [Thanks to Taylor Lowry for this other one!]
 ((22  2) / 2) ^ 2 = 100 [Thanks to Karen D. Miller for this other one!]
 6! / 6  6! / (6 * 6) = 100 [Thanks to Karen D. Miller for this other one!]
 5!  5  5  5  5 = 100 [Thanks to Karen D. Miller for this other one!]
 5!  (5 + 5 + 5 + 5) = 100 [Thanks to Jim St. Clair for this other one!]
 5 * 5 * (5  5 / 5) = 100 [Thanks to Rishi Mohan Sanwal for this one!]
 4! + 4! + 4! + 4! + 4 = 100 [Thanks Karen D. Miller and Saurabh Gupta!]
 99 + 9 ^ (9  9) = 100 [Thanks Gopalakrishnan Thirumurthy for this one!]
 5!  5 * (5  5 / 5) = 100 [Thanks Gopalakrishnan Thirumurthy for it!]
 (4! + 4 ^ (4  4)) * 4 = 100 [Thanks Gopalakrishnan Thirumurthy for it!]
 4! * 4 + 4  4 + 4 = 100 [Thanks Gopalakrishnan Thirumurthy for it!]
 (4! * 4) + (4 * 4 / 4) = 100 [Thanks Gopalakrishnan Thirumurthy for it!]
 5 * 5 * (5  (5  5)!) = 100 [Thanks Gopalakrishnan Thirumurthy for it!]
 ((9  9) */ 9)! + 99 = 0! + 99 = 1 + 99 = 100 [Thanks to Bala Neerumalla!]
 (3  3)! + 33 * 3 = 100 [Thanks Bala Neerumalla for this other one!]
 (5 + 5) ^ ((5 + 5) / 5) = 100 [Thanks Bala Neerumalla for this one!]
 ((2 ^ 2) * 2 + 2) ^ 2 = 100 [Thanks Bala Neerumalla for this one!]
 (4! + ((4  4) */ 4)!) * 4 = 100 [Thanks Bala Neerumalla for this one!]
Glen Parnell points out that, in any solution in which the digit 2 is used, it could be replaced by 2!, whenever the 2 is not only a digit but also a number, as 2 = 2! (but of course, 22 is not equal to 22!).
Bala Neerumalla has suggested some alternative solutions using trigonometric functions Sin() and Cos():
 Sin(99  9) + 99 = Sin(90) + 99 = 1 + 99 = 100
 Cos((9  9) */ 9) + 99 = Cos(0) + 99 = 1 + 99 = 100
 Cos(3  3) + 33 * 3 = 100
 (4! + (Sin(44)*4)!)*4 = 100
 88 + 8 + CR(8) + CR(8) = 100
 (8 + CR(8)) ^ (CR(8) * (8 / 8)) = 100
 ((CR(8) * CR(8) * CR(8)) + CR(8)) ^ CR(8) = 100
 ((8 * (8 / 8)) + CR(8)) ^ CR(8) = 100
Bala Neerumalla smartly noticed that he can produce number 100 by using a different number base than the normal base 10 (b10). The following example is in base 5 (b5):
 444  44 = (4 * 5^2 + 4 * 5^1 + 4 * 5^0)  (4 * 5^1 + 4 * 5^0) = 100
 111  11 = 100 [Wolfgang Solfrank pointed out that this works in any number base, thanks!]
 b16 4 ^ 4 + 4 * (4  4) = 100 [Thanks to Glen Parnell for this one!]
 b16 (2 * 2 * 2 * 2) ^ 2 = 100 [Thanks to Glen Parnell for this one!]
 b8 4 * 4 * 4 + (4  4) = 100 [Thanks to Glen Parnell for this one!]
 b8 (4 ^ 4) / 4 + (4  4) = 100 [Thanks to Glen Parnell for this one!]
 b8 4 * 4 * 4 * (4 / 4) = 100 [Thanks to Glen Parnell for this one!]
 b8 (2 ^ (2 * 2)) * 2 * 2 = 100 [Thanks to Glen Parnell for this one!]
 b2 11  1 + 1 + 1 = 100 [Thanks to Glen Parnell for this one!]
 bX+1 ((X  X) */ X)! + XX = 100
 b16 ((F  F) */ F)! + FF = 100
 b12 ((B  B) */ B)! + BB = 100
 b10 ((9  9) */ 9)! + 99 = 100 [As already shown by Bala Neerumalla]
 b8 ((7  7) */ 7)! + 77 = 100
 b4 ((3  3) */ 3)! + 33 = 100
 b2 ((1  1) */ 1)! + 11 = 100
 ((L / L) + (L / L)) * L = ((50 / 50) + (50 / 50)) * 50 = 100
 (C / C) * (C / C) * C = (100 / 100) * (100 / 100) * 100 = 100
 (C / C)  (C / C) + C = (100 / 100)  (100 / 100) + 100 = 100
 CCC  CC = 300  200 = 100
 CC  CC + C = 200  200 + 100 = 100
 (L + L) * L ^ (L  L) = (50 + 50) * 50 ^ (50  50) = 100
 (L + L) / L ^ (L  L) = (50 + 50) / 50 ^ (50  50) = 100
 XX * X  X * X = 20 * 10  10 * 10 = 100
 (X + (X / X)) * X  X = (10 + (10 / 10)) * 10  10= 100
 X * X * (X ^ (X  X)) = 10 * 10 * (10 ^ (10  10) = 100
 X * X / (X ^ (X  X)) = 10 * 10 / (10 ^ (10  10) = 100
 C * C * C / C * C = 100 * 100 * 100 / 100 * 100 = 100
 (C  C) + (C  C) + C = (100  100) + (100  100) + 100 = 100
 L * (L  L) + L + L = 50 * (50  50) + 50 + 50 = 100
 C * (CC / C)  C = 100 * (200 / 100)  100 = 100
 C * (C / C) + (C  C) = 100 * (100 / 100) + (100  100) = 100
Now, how about some solution using Roman numerals 'D' (500), or 'M' (1000)? If you find any alternative solutions, get in touch with us by email!
Easy!
Tuesday, November 4, 2014
A Thinking Man
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5:29 AM
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Professor Percent was a maths lecturer with an interest for new ways to express
mathematical expressions. The traditional symbols (+, , *, /, etc) were not
enough anymore, to convey his superior numeric operations, so he had to invent
new symbols, and only a superior brain would be able to understand the need
for his new symbols.
The first symbol he invented was §; between two numbers, it meant that, if the first number was greater than the second, then the second should be subtracted from the first one; otherwise the two numbers should be added. Therefore 5 § 2 = 3, while 2 § 5 = 7.
The poor people that had to put up with this were, of course, his students. In the last test they were faced with:
5 ¿ 2 = 27
6 ¿ 3 = 27
8 ¿ 4 = 36
and also with:
5 ¤ 2 = 15
6 ¤ 4 = 12
3 ¤ 8 = 40
What are the meanings of the symbols ¿ and ¤?
The first symbol he invented was §; between two numbers, it meant that, if the first number was greater than the second, then the second should be subtracted from the first one; otherwise the two numbers should be added. Therefore 5 § 2 = 3, while 2 § 5 = 7.
The poor people that had to put up with this were, of course, his students. In the last test they were faced with:
5 ¿ 2 = 27
6 ¿ 3 = 27
8 ¿ 4 = 36
and also with:
5 ¤ 2 = 15
6 ¤ 4 = 12
3 ¤ 8 = 40
What are the meanings of the symbols ¿ and ¤?
Notes:
There are at least 3 different solutions for ¿.
A Thinking Man Puzzle Solution
The symbol ¿ means the difference between the number made up of the all digits of the operation, and the mirror of this last number. i.e,5 ¿ 2 = 52  25 = 27
6 ¿ 3 = 63  36 = 27
8 ¿ 4 = 84  48 = 36
An alternative solution for this symbol (submitted by Alfa Chan... many thanks!) is simply the difference between the two numbers multiplied by 9. i.e,
5 ¿ 2 = (5  2) × 9 = 27
6 ¿ 3 = (6  3) × 9 = 27
8 ¿ 4 = (8  4) × 9 = 36
Another alternative solution submitted by Mickey Kawick... thanks!! We have x ¿ y; If x is odd, then the result is 5x + y, otherwise it's 5x  y. i.e,
5 ¿ 2 = 5 × 5 + 2 = 27 (5 is odd, so we add the 2)
6 ¿ 3 = 6 × 5  3 = 27 (6 is even, so we subtract the 3)
8 ¿ 4 = 8 × 5  4 = 36 (8 is even, so we subtract the 4)
The symbol ¤ means the difference between the two numbers multiplied by the larger of the two numbers. i.e,
5 ¤ 2 = (5  2) * 5 = 3 * 5 = 15
6 ¤ 4 = (6  4) * 6 = 2 * 6 = 12
3 ¤ 8 = (8  3) * 8 = 5 * 8 = 40
An alternative solution for this symbol, as submitted by Jeff Schall (many thanks!), is the difference between the square of the bigger of the two numbers and their product. i.e,
5 ¤ 2 = (5 ^ 2)  (5 * 2) = 25  10 = 15
6 ¤ 4 = (6 ^ 2)  (6 * 4) = 36  24 = 12
3 ¤ 8 = (8 ^ 2)  (3 * 8) = 64  24 = 40
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