Squares vs Cubes From Asim Shah: Find the two smallest numbers whose difference between their squares is a cube and whose difference between their cubes is a square. As a hint and encouragement, both numbers are between 3 and 12. The next such pair is 384, 640. 4A = 6V George Sicherman has shown that 4A = 6V. Red Green Blue Maze Chris Lusby Taylor: I've just been asked to do something for a local school's playground. I planned to use the existing paving slabs as squares but then found that they're laid in an offset pattern, so each has six neighbours. Enter at the top, cross the blue, green, and red bars, and keep this sequence until you exit at the bottom. Or enter at the bottom, and cross the red green and blue bars, and keep this sequence until you exist at the top. A problem of squares Bernardo Recamán Santos: Find a four-digit square number which has at least one digit in common with every other four-digit square number. Toothpick Giraffe Puzzle. Five toothpicks form the giraffe shown above. Change the position of just one pick and leave the giraffe in exactly the same form as before. The re-formed animal may alter its orientation or be mirror reversed but must have its pattern unchanged. The Zen of Labyrinth Robert Abbott: Dave Phillips wrote a new maze book called "The Zen of the Labyrinth." I reviewed it here: http://www.logicmazes.com/reviews.html I thought one of his mazes would look great on mathpuzzle.com, so a GIF of the maze is the first attachment here. Dave says you have his permission to use the maze. These are the rules: Enter by the bottom red path and end on the center gray square. You may retrace your path but may not make a U-turn on a pathway. You must follow the paths in the order red, blue, yellow and then red, blue, yellow again, as needed, changing color on the white squares. NPR Puzzle The puzzle from NPR this week is mine. "This challenge comes with help from math puzzle expert Ed Pegg. Take the names of the first nine elements of the periodic table: hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen and fluorine. Select one letter from each of these names in order to spell a familiar nine-letter word. Hint: It's a word used in math." Send Answer. Here's a similar puzzle that Will Shortz though was slightly too obscure: Take the names of the officially recognized planets in order, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Select one letter from each of these names in order to spell a familiar eight-letter name. Hint: It's a name used in math. Answer. Erich Friedman Puzzles Erich Friedman: Multi-Balance Puzzles, Pyramid Puzzles, Crypto-Product Puzzles, Weight Equation Puzzles, Gold Star Puzzles, and Packing Puzzles have been added to Erich's Puzzle Palace. For example, for Weight Equations, put a digit in each box so that the equation is true. The boxes should also balance, where each digit represents the weight of that box. (His entry on Packing Problems at Math Magic this month is also very nice.) Late Christmas Tree Serhiy Grabarchuk: Here is a Strimko inspired Christmas tree. 24 from 8,8,3,3 Puzzles -> Number Puzzles How can I get the answer 24 by only using the numbers 8,8,3,3. You can use the main signs add, subtract multiply and divide. Answer 8/(3-(8/3)) = 8/(1/3) = 24 5-digit Number What 5-digit number has the following features: If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number? Answer Using an easy equation: 3(100000 + x) = 10x+1 (Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number) Solving this gives: 10x+1 = 3(100000 + x) 10x+1 = 300000 + 3x 10x = 299999 + 3x 7x = 299999 x= 299999/7 = 42857 The answer is 42857. Birthday Puzzles -> Number Puzzles When asked about his birthday, a man said: "The day before yesterday I was only 25 and next year I will turn 28." This is true only one day in a year - when was he born? Answer: He was born on December 31st and spoke about it on January 1st. Choose the Right Symbol - Solution Puzzles -> Number Puzzles The Puzzle: What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9? Answer A Decimal Point 5.9 works nicely The Puzzle: A popular mathematical pastime: Use exactly four 4's to form every integer from 0 to 50, using only the operators +, -, x, /, () (brackets) x2 (square), and ! (factorial). Example: 0 = 44-44 Answer 0 = 44-44 1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4) 2 = 4/4+4/4 3 = (4+4+4)/4 4 = 4*(4-4)+4 5 = (4*4+4)/4 6 = 4*.4+4.4 7 = 44/4-4 8 = 4+4.4-.4 9 = 4/4+4+4 10 = 44/4.4 11 = 4/.4+4/4 12 = (44+4)/4 13 = 4!-44/4 14 = 4*(4-.4)-.4 15 = 44/4+4 16 = .4*(44-4) 17 = 4/4+4*4 18 = 44*.4+.4 19 = 4!-4-4/4 20 = 4*(4/4+4) 21 = (4.4+4)/.4 22 = 44*sqrt(4)/4 23 = (4*4!-4)/4 24 = 4*4+4+4 25 = (4*4!+4)/4 26 = 4/.4+4*4 27 = 4-4/4+4! 28 = 44-4*4 29 = 4/.4/.4+4 30 = (4+4+4)/.4 31 = (4!+4)/4+4! 32 = 4*4+4*4 33 = (4-.4)/.4+4! 34 = 44-4/.4 35 = 44/4+4! 36 = 44-4-4 37 = (sqrt(4)+4!)/sqrt(4)+4! 38 = 44-4!/4 39 = (4*4-.4)/.4 40 = 44-sqrt(4*4) 41 = (sqrt(4)+4!)/.4-4! 42 = sqrt(4)+44-4 43 = 44-4/4 44 = 44.4-.4 45 = 4/4+44 46 = 44-sqrt(4)+4 47 = 4!+4!-4/4 48 = 4*(4+4+4) 49 = (4!-4.4)/.4 50 = 4!/4+44 Fraction - Solution Puzzles -> Number Puzzles The Puzzle: Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals exactly 1/3 (one third)? Example that doesn't work: 7192/38456 = 0.187 . . . . (Scroll down if you really want to see the Solution ...) . . . . . . The Solution . . . 5832/17496 = 1/3 Tricky Equation - Solution Puzzles -> Number Puzzles The Puzzle: The following equation is wrong: 101 - 102 = 1 Move one numeral to make it correct. (Caution: Trick) . . . . (Scroll down if you really want to see the Solution ...) . . . . . . The Solution . . . Move the numeral 2 half a line up to achieve 101-102 = 1 Cut Cube - Solution Puzzles -> Logic Puzzles The Puzzle: A solid, four-inch cube of wood is coated with blue paint on all six sides. Then the cube is cut into smaller one-inch cubes. These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be? . . . . (Scroll down if you really want to see the Solution ...) . . . . . . The Solution . . . There are 24 with one side colored, 8 with three sides colored, 24 with two sides colored, and 8 with no sides colored. Explain: Elevator - Solution Puzzles -> Logic Puzzles The Puzzle: A Man works on the 10th floor and always takes the elevator down to ground level at the end of the day. Yet every morning he only takes the elevator to the 7th floor and walks up the stairs to the 10th floor, even when is in a hurry. Why? . . . . (Scroll down if you really want to see the Solution ...) . . . . . . The Solution . . . He is too short to reach the "10" button. The Puzzle: A man walks into a bar and asks the bartender for a glass of water. But the bartender takes out a gun and aims it at the man's head. The man says "Thank You" and walks out. Why? . . . . (Scroll down if you really want to see the Solution ...) . . . . . . The Solution . . . The man had hiccups. He wanted to cure it with a glass of water, but the bartender cured it by giving him a surprise.