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Mathematical Brainteasers with Surprising Solutions
Proves that math can be serious fun!
If you like any kind of game at all, you'll enjoy the amazing mathematical brainteasers in this entertaining book. No special mathematics training is needed.
With an emphasis on puzzling word problems with surprising solutions, the author presents his mathematical hurdles in order of increasing difficulty. Many appear deceptively simple, such as: How many quarter-inch marks are on an unusual sixteen-inch ruler? Or: If the cost of a bottle and a cork is $1.10 and the bottle costs $1.00 more than the cork, how much did the bottle alone cost? Check the answers before you decide that these are too easy. You may be surprised.
Novices may want to begin with some of the teasers in the first "easy" section. More experienced math-heads may want to test their wits with the "challenging" or even the "difficult" sections (some are fiendishly difficult). Including word problems by famed mathematical puzzle geniuses Sam Loyd (1841 - 1911) and Henry Ernest Dudeney (1857 - 1930), which have entertained recreational math aficionados for more than a century, this book has something for puzzle solvers at any level. And for the math phobic, it may whet your appetite to delve into a subject you thought could only be boring.
If you like any kind of game at all, you'll enjoy the amazing mathematical brainteasers in this entertaining book. No special mathematics training is needed.
With an emphasis on puzzling word problems with surprising solutions, the author presents his mathematical hurdles in order of increasing difficulty. Many appear deceptively simple, such as: How many quarter-inch marks are on an unusual sixteen-inch ruler? Or: If the cost of a bottle and a cork is $1.10 and the bottle costs $1.00 more than the cork, how much did the bottle alone cost? Check the answers before you decide that these are too easy. You may be surprised.
Novices may want to begin with some of the teasers in the first "easy" section. More experienced math-heads may want to test their wits with the "challenging" or even the "difficult" sections (some are fiendishly difficult). Including word problems by famed mathematical puzzle geniuses Sam Loyd (1841 - 1911) and Henry Ernest Dudeney (1857 - 1930), which have entertained recreational math aficionados for more than a century, this book has something for puzzle solvers at any level. And for the math phobic, it may whet your appetite to delve into a subject you thought could only be boring.
208 pages, Paperback
Published November 12, 2019
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Displaying 1 - 4 of 4 reviews
March 22, 2023
3.5 stars. Humbling to say the least
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November 4, 2023[SPOILERS] Here are some (not all) errors (outright or merely editorial):
- Puzzle 30, Pg 66 [editorial]. The solution can work if the track is curved in a way that allows a 'short cut' for the fly, or if the fly cannot make contact with physical matter (it is stated that the fly is "directly [in] front of one train"). However, if the fly can make contact with physical matter and it either travels between trains along the track or if the track is not curved in a way that would allow a ‘short cut’ between the trains, then this puzzle does not work as worded.
- Puzzle 32, Pg 70 [editorial]: This is exactly the famous Monty Hall problem, only with doors replaced by cards and goats and prizes replaced by particular card faces. Since this is such a famous mathematical problem, some reference should be made to it in the solution, by name. Instead, the citation is just to the author himself.
- Puzzle 36, Pg 78 [outright]: The solution has the phrase “If the average paid to all 30,000 residents was $1,000, the total paid out would have been $30,000”. Thirty thousand multiplied by one thousand is thirty million, not thirty thousand. This mistake propagates to the solution itself, which is $20,000,000, not $20,000.
- Puzzle 37, Pg 80 [editorial]: The figure that is part of the question should be printed on the page with the question, not on the page with the solution. There was ample room on the former.
- Puzzle 37, Pg 80 [outright/editorial]: The solution describes the formula ab/a+b as if it is ab/(a+b), which is not the same thing.
- Puzzle 61, Pg 145 [editorial]: The phrase “99% of the potatoes consist of water” by itself may refer to mass or volume. It is obvious from the solution that it must refer to mass (unless the density of the solid part and water are somehow equal), but this should have been made clearer
- Puzzle 62, Pg 148 [outright]: While the overall structure of this solution is quite nice, one cannot just decide to walk 12 yards from point E to D and *then* “[line] up D with C and B”, as if were even possible to post hoc force three arbitrary points onto a line! The line from B to C intersects some point west of E, certainly, but one cannot know that point a priori — one has to measure it, and we are given no information in the question that would allow us to do so.
- [editorial] Not so much an error, but there are several instances where puzzles essentially repeat themselves through the book, sometimes in short succession. For example, puzzles 68 and 71 are essentially the same puzzle. Puzzles 20, 31, and 89 are also essentially the same puzzle or at least is approached the same way (strangely, the latter, in the section marked most challenging, may be easier than the other two). Puzzles 92 and 93 are essentially identical puzzles (back-to-back) involving (but not naming) Bayes’ rule. Here is a puzzle for you: What is the probability that, among 121 puzzles, at least three pairs of puzzles will be identical?
- Puzzle 91, Pg 217 [editorial]: Not technically an error but this puzzle is in the section identified as the most challenging, but it is literally “what is 70 percent of 35”?
- Puzzle 93, Pg 222 [outright]: It is claimed that 90% of 8 is 7 (it is 7.2). This may be excused because later another fraction is rounded explicitly. Later in the same puzzle we have a set of 77 women with diagnoses, only 7 of whom have the disease. The probability that anyone in this set actually has the disease is 7/77, not 7/70 as is claimed.
- Puzzle 30, Pg 66 [editorial]. The solution can work if the track is curved in a way that allows a 'short cut' for the fly, or if the fly cannot make contact with physical matter (it is stated that the fly is "directly [in] front of one train"). However, if the fly can make contact with physical matter and it either travels between trains along the track or if the track is not curved in a way that would allow a ‘short cut’ between the trains, then this puzzle does not work as worded.
- Puzzle 32, Pg 70 [editorial]: This is exactly the famous Monty Hall problem, only with doors replaced by cards and goats and prizes replaced by particular card faces. Since this is such a famous mathematical problem, some reference should be made to it in the solution, by name. Instead, the citation is just to the author himself.
- Puzzle 36, Pg 78 [outright]: The solution has the phrase “If the average paid to all 30,000 residents was $1,000, the total paid out would have been $30,000”. Thirty thousand multiplied by one thousand is thirty million, not thirty thousand. This mistake propagates to the solution itself, which is $20,000,000, not $20,000.
- Puzzle 37, Pg 80 [editorial]: The figure that is part of the question should be printed on the page with the question, not on the page with the solution. There was ample room on the former.
- Puzzle 37, Pg 80 [outright/editorial]: The solution describes the formula ab/a+b as if it is ab/(a+b), which is not the same thing.
- Puzzle 61, Pg 145 [editorial]: The phrase “99% of the potatoes consist of water” by itself may refer to mass or volume. It is obvious from the solution that it must refer to mass (unless the density of the solid part and water are somehow equal), but this should have been made clearer
- Puzzle 62, Pg 148 [outright]: While the overall structure of this solution is quite nice, one cannot just decide to walk 12 yards from point E to D and *then* “[line] up D with C and B”, as if were even possible to post hoc force three arbitrary points onto a line! The line from B to C intersects some point west of E, certainly, but one cannot know that point a priori — one has to measure it, and we are given no information in the question that would allow us to do so.
- [editorial] Not so much an error, but there are several instances where puzzles essentially repeat themselves through the book, sometimes in short succession. For example, puzzles 68 and 71 are essentially the same puzzle. Puzzles 20, 31, and 89 are also essentially the same puzzle or at least is approached the same way (strangely, the latter, in the section marked most challenging, may be easier than the other two). Puzzles 92 and 93 are essentially identical puzzles (back-to-back) involving (but not naming) Bayes’ rule. Here is a puzzle for you: What is the probability that, among 121 puzzles, at least three pairs of puzzles will be identical?
- Puzzle 91, Pg 217 [editorial]: Not technically an error but this puzzle is in the section identified as the most challenging, but it is literally “what is 70 percent of 35”?
- Puzzle 93, Pg 222 [outright]: It is claimed that 90% of 8 is 7 (it is 7.2). This may be excused because later another fraction is rounded explicitly. Later in the same puzzle we have a set of 77 women with diagnoses, only 7 of whom have the disease. The probability that anyone in this set actually has the disease is 7/77, not 7/70 as is claimed.
April 16, 2023
Author Owen O'Shea collected 121 puzzles and brainteasers with counterintuitive solutions. O'Shea draws the puzzles from various sources.
I encountered some of these puzzles before, or at least the general idea behind them. None of the puzzles require advanced mathematics.
The book makes for a good collection. Thanks for reading my review, and see you next time.
I encountered some of these puzzles before, or at least the general idea behind them. None of the puzzles require advanced mathematics.
The book makes for a good collection. Thanks for reading my review, and see you next time.
October 19, 2023
This is an interesting and fun book of mathematical and logic puzzles which are mostly surprising. Some questions require a rudimentary understanding of geometry and algebra but most don't require advanced ability. But some puzzles aren't that intuitive. The biographies at the end remind the reader the seedier side of the math puzzles world.
Displaying 1 - 4 of 4 reviews