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  1. K

    Product equality and sum of squares equality puzzle

    Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. ABCD*EF=GHJB*KE, and: (EH)2 + (KC)2 = (KH)2
  2. K

    Two successive digits and divisibility puzzle

    Determine all possible value(s) of a 8-digit base 10 positive integer having the form ABCDEFGH, where each of the capital letters denotes a different digit from 1 to 9, that satisfy each of the following conditions: (I) AB is divisible by 2, and: (II) BC is divisible by 6, and: (III) CD...
  3. K

    Product Equality and Linear Expression Puzzle

    Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. (ABC)*(DE)=(BCD)*(BF), and: FA+DF- CE=1
  4. K

    Sum, difference and equality puzzle

    Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. GEORGE + RUGGLE + 15750 + 16220 + P = PPPPPP, and: OE - LR = LO, and: RUGGLE is divisible by 7
  5. K

    TV series and competition puzzle

    In this season's "Dancing with the Celebs" TV series, Harry and nine other famous personalities paired with professional dancers to try to claim this year's title. Each week, one of the celebrities--who are in different entertainment and media fields, with one a stand-up comic--is sent home...
  6. K

    Three Passengers and Train Station Puzzle

    Brian, Amy and Stephanie are waiting at the train station. Each of the three is waiting for a different train. When they check the station clock, they realize that Amy is going to have to wait twice as long for her train as Brian will for his, while Stephanie will have to wait twice as long...
  7. K

    Product equality and difference puzzle

    Substitute each of the capital letters by a base ten digit from 0 to 9 to satisfy this set of cryptarithmetic equations. None of the numbers can contain any leading zero. ABC*D=C*BCD, and: BC-CA-AD= 5
  8. K

    2010 and sum of digits puzzle

    Determine the sum of all the digits in the positive integers from 1 to 2010 inclusively.
  9. K

    Knight and knaves and distant planet puzzle

    A distant planet is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. Eight inhabitants of the planet: Marge, Mel, Betty, Bob, Bill, Carl, Zeke and Alice are busy at a conversation, when a visitor from a neighboring planet stops by and asks each of...
  10. K

    Infinite String and Letter Puzzle

    The string abbcccddddeeeee… continuously repeats such that after the final z, the letters abbcccddddeeeee… begin again. What will be the 3000th letter in the pattern?
  11. K

    Six Jars and Arsenic Puzzle

    Six jars are placed (left to right: coffee, arsenic, and sugar on the top shelf; snuff, tea, and salt on the bottom shelf) and, thereafter filled up with these ingredients, making sure each jar contains something other than what the label says. It is known that: (i) The salt is located...
  12. K

    Sum of Four Squares and Digits Puzzle

    Substitute each of the small letters by a different base ten digit from 1 to 9, with a<= b<=c<=d, to satisfy this equation. a2 + b2 + c2 + d2 = e2
  13. K

    Four contestants and three statements puzzle

    Four contestants E, F, G, and H ran for a contest. When asked by a common acquaintance, three spectators A, B, C made the following statements regarding the final results. 1. A said, "Either E or H is the winner." 2. B said, "E is not the winner." 3. C said, "Neither H nor G is the...
  14. K

    Line and Letter Placement Puzzle

    Does the letter R go above or below the line? A B D O P Q __________________ C E F G H I J K L M N
  15. K

    Square Grid and Letter Assignment Puzzle

    Place the letters A, B, C, D, E, F, G, H and I into a 3x3 square grid with each square containing a different letter, using the following information: (i) I is in the same column as E which is not in the center column. (ii) D is in the row below the row which contains F. (iii) A is in...
  16. K

    Bus ticket and sum of digits puzzle

    Yesterday Professor Q rode on a bus with his friend. As soon as he got the tickets for himself and his friend, which were consecutively numbered with each of the tickets bearing a 5-digit number with no leading zero, he added the digits on them and told his friend that the sum of all ten digits...
  17. K

    Birthday Gift Puzzle

    Albert, Bob and Cal each gave a birthday gift to their friend Don, who was so impressed by the presents, that he exclaimed: "Good thing your parents gave you credit cards!" Bob explained that those cards had already been confiscated by the parents of each, and that they had to spend cold...
  18. K

    Two friends and age puzzle

    Two friends Andy and Cal form a team together. Andy is as old as Cal will be when Andy is twice as old as Cal was when Andy was half as old as the sum of their current ages. Cal is as old as Andy was when Cal was half as old as he will become in ten years. Determine the respective current...
  19. K

    Analog Clock and Minute Marks Puzzle

    The minute hand of a 12 hour analog clock is situated precisely on a minute mark, while the hour hand is situated exactly 2 minute marks behind the minute hand. What time is it? Note: For purposes of the problem, each hour mark is deemed as a valid minute mark.
  20. K

    Even Perfect and Prime Puzzle

    Determine all possible even perfect number(s) C such that each of C-1 and C+1 is a prime number.
  21. K

    Power and value assignment puzzle

    Substitute each capital letter in bold by a different digit from 0 to 9, such that (TAU).BETA when rounded off to the nearest integer is equal to PI, and the absolute difference of (TAU).BETA and PI is the minimum. Each of T, B and P is nonzero.
  22. K

    Row total and column total puzzle

    Arrange the nine cells of a 3x3 square with digits from 1 to 9, with each digit occurring exactly once, such that: ## The respective totals of the first column, second column and the third column are 15, 19 and 11, and: ## The respective totals of the first row, second row and the...
  23. K

    Repaid and Ratio Puzzle

    Substitute each of the letters by a different digit from 0 to 9 to satisfy this equation. None of the four numbers can contain any leading zero. (REPAID)/(DIAPER) = (RA)/(RE) Note: Each of the four numbers represent the concatenation of the digits, and does not denote the product of the...
  24. K

    3x3 square and common sum puzzle

    Substitute each of the capital letters by a different digit from 0 to 9, such that each of the columns, each of the rows and each of the two main diagonals of this 3x3 square have the common sum LRK. It is known that L is nonzero and, each of the numbers in the nine cells contains non leading...
  25. K

    Squares, subsquares and arrangement puzzle

    Substitute each of the capital letters in this 3x3 square by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subsquares is equal to 6*E. A B C D E F G H I What will be the arrangement(s), if keeping all the other conditions unaltered, the...
  26. K

    Rare and Meer Puzzle

    Determine the value of each of the four perfect squares MEER, EMMA, EMIR and RARE, where each of the capital letters denotes a different digit from 0 to 9. None of the four numbers contains any leading zero.
  27. K

    Twelve Sum and Digit Substitution Puzzle

    Substitute each of the capital letters in the figure given below by a different digit from 0 to 7 such that: A+B+C = A+D+F = C+E+H = F+G+H = 12. A B C D E F G H Note: The rotations and reflections of a valid arrangement are deemed as the same solution.
  28. K

    Hundred Sum and Prime Puzzle

    Substitute each of the capital letters by a different digit from 1 to 9 to satisfy this cryptarithmetic equation: (P*Q)/R + (S*T*U)/V + W*X = 100, where the 2-digit number WR is prime.
  29. K

    Train station, speed and time puzzle

    George took a train at station X with the intention of going to Station Y (which is located 8 kilometers from station X). At the precise instant that the train started leaving station X, the minute hand of his 12 hour analog wristwatch was located precisely on a minute mark. George looked at...
  30. K

    Abababcb and perfect square puzzle

    P is a base ten positive integer of the form abababcb, such that (P-1) is a perfect square ; where a, b and c denote three different digits from 0 to 9, with a being nonzero. Determine all possible value(s) of P for which this is possible.
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