Author Archives: Jim Stevenson

Date Night

This is a fairly straight-forward logic puzzle from Alex Bellos’s Monday Puzzle in The Guardian.

“When it comes to the world of mathematical puzzles, Hungary is a superpower. Not just because of the Rubik’s cube, the iconic toy invented by Ernő Rubik in 1974, but also because of its long history of maths outreach.

In 1894, Hungary staged the world’s first maths competition for teenagers, four decades before one was held anywhere else. 1894 also saw the launch of KöMaL, a Hungarian maths journal for secondary school pupils full of problems and tips on how to solve them. Both the competition and the journal have been running continuously since then, with only brief hiatuses during the two world wars.

This emphasis on developing young talent means that Hungarians are always coming up with puzzles designed to stimulate a love of mathematics. (It also explains why Hungary arguably produces, per capita, more top mathematicians than any other country.)

I asked Béla Bajnok, a Hungarian who is now director of American Mathematics Competitions, a series of competitions involving 300,000 students in the US, whether he knew of any puzzles that originated in Hungary. The first thing he said that came to mind was the ‘3-D logic puzzle’, a type of logic puzzle in which you work out the solution in a three dimensional box, rather than (as is the case with the standard version) in a two-dimensional grid. He said he had never seen this type of puzzle outside Hungary.

Below are two examples he created. You could solve these using an extended two dimensional grid. It’s more in the spirit of the question, however, to draw a three-dimensional one, like you are looking at three sides of a Rubik’s Cube.

Date night

Andy, Bill, Chris, and Daniel are out tonight with their dates, Emily, Fran, Gina, and Huong. We have the following information.

  1. Andy will go to the opera
  2. Bill will spend the evening with Emily,
  3. Chris would not want to go out with Gina,
  4. Fran will see a movie
  5. Gina will attend a workshop.

We also know that one couple will see an art exhibit. Who will go out with whom, and what will they do?”

See Date Night

Meeting on the Bridge

Here is another Brainteaser from the Quantum math magazine.

“Nick left Nicktown at 10:18 A.M. and arrived at Georgetown at 1:30 P.M., walking at a constant speed. On the same day, George left Georgetown at 9:00 A.M. and arrived at Nicktown at 11:40 A.M., walking at a constant speed along the same road. The road crosses a wide river. Nick and George arrived at the bridge simultaneously, each from his side of the river. Nick left the bridge 1 minute later than George. When did they arrive at the bridge?”

Answer.

See Meeting on the Bridge for solutions.

Clock Connections Puzzle

This is an imaginative puzzle from the Maths Masters team, Burkard Polster (aka Mathologer) and Marty Ross as part of their “Summer Quizzes” offerings for 2012.

“You draw a line connecting the 5 and 9 on a clock face, and another line connecting the 3 and 8. What is the angle between the two lines?”

Answer.

See the Clock Connections Puzzle for solutions.

Turning Wheels Puzzle

This is a thoughtful little problem from Posamentier’s and Lehmann’s Mathematical Curiosities.

“We have nine wheels touching each other with diameters successively increasing by 1 cm. Beginning with 1 cm as the smallest circle, and 9 cm for the largest circle, how many degrees does the largest circle turn when the smallest circle turns by 90°?”

Answer.

See the Turning Wheels Puzzle for solutions.

Point of Intersection Problem

I came across an interesting problem in the MathsJam Shout for February 2022.

(“MathsJam is a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like.  Puzzles, games, problems, or just anything they think is cool or interesting.  Monthly MathsJam nights happen in over 70 locations around the world, on the second-to-last Tuesday of each month.  To find your nearest MathsJam, visit the website at www.mathsjam.com.”)

“Given two lines Ax + By + C = 0 and ax + by + c = 0, is there a simple link between the vectors (A, B, C), (a, b, c), and the point where the lines cross?”

The answer, of course, is yes, but the question is somewhat open-ended and I was not able to track down any answer given.

See the Point of Intersection Problem

An Intercept Problem

This is a straight-forward problem by Geoffrey Mott-Smith from 1954.

“Three tangent circles of equal radius r are drawn, all centers being on the line OE. From O, the outer intersection of this axis with the left-hand circle, line OD is drawn tangent to the right-hand circle. What is the length, in terms of r, of AB, the segment of this tangent which forms a chord in the middle circle?”

Answer.

See An Intercept Problem for solutions.

Two Candles

This is another candle burning problem, presented by Presh Talwalkar.

“Two candles of equal heights but different thicknesses are lit. The first burns off in 8 hours and the second in 10 hours. How long after lighting, in hours, will the first candle be half the height of the second candle? The candles are lit simultaneously and each burns at a constant linear rate.”

Answer.

See Two Candles for solutions.

Seven Girls Puzzle

This problem comes from the Scottish Mathematical Council (SMC) Senior Mathematical Challenge of 2007:

“A group of seven girls—Ally, Bev, Chi-chi, Des, Evie, Fi and Grunt—were playing a game in which the counters were beans. Whenever a girl lost a game, from her pile of beans she had to give each of the other girls as many beans as they already had. They had been playing for some time and they all had different numbers of beans. They then had a run of seven games in which each girl lost a game in turn, in the order given above. At the end of this sequence of games, amazingly, they all had the same number of beans—128. How many did each of them have at the start of this sequence of seven games?”

Answer.

See the Seven Girls Puzzle for solutions.

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