Math Puzzles II

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A collection of math puzzles for fun and pleasure! Tease your brain with these math puzzles, then click to show or hide the answer. (Note: You may need to enable JavaScript on your browser for the answers to show properly.)

Also visit our Math Trivia page for more arithmetic riddles, geometry riddles, statistics riddles, calculus riddles etc.

1. Love Boat

   A young man decided to impress his girlfriend with his new speedboat, and so he arranged to meet her on the riverbank, 24 miles upstream. Normally, his boat could go at 14 miles an hour, but he soon realized that the current was running 4 miles an hour against him. He has 20 gallons of fuel in his tank, but he uses up 6 gallons an hour. Does he make it or does he run out of fuel? He makes it with more than 5 gallons to spare.

2. Nice Try

   Maria’s real age has long been shrouded in mystery. Whenever anyone asked her, she would say that she was thirty, mentally omitting all Sundays. Sundays she didn’t work, she said, so naturally she didn’t get any older. How old was she really? Maria is 35. She subtracted one-seventh of her real age. Now try the second question: Why bother?

3. Jack And Jill Ran Up The Hill

   Jack and Jill were racing up the hill, but it was no contest. Jack won by a good 10 yards on their 100-yard run. Jill suggested that in their next race, Jack should start 10 yards behind their starting line. She reasoned that this would make it fairer. Who won the second race, and by how much? Jack still won by 1 yard. He can run 100 yards in the time it takes Jill to run 90, so he can run his remaining 10 yards while Jill runs 9.

4. The Constant Tin Soldier

   John was having a hard time lining up his tin soldiers. He didn’t have that many (fewer than a hundred) but he couldn’t seem to arrange them in parade properly. He kept having odd numbers left over. He tried rows of 5 and there were 4 left over – rows of 6, 4 left over – rows of 7, 1 left over. He finally decided to have a very narrow parade and arranged them in rows of 4. This time it worked. What is the smallest number of tin soldiers he could have? 64

5. Car Scam

   You fill up the gas tank of your nice new small car, which holds 10 gallons and gives 25 miles to the gallon, and go on a road trip. This should easily get you to your first stop, which is 225 miles away. Unfortunately, about 20 miles from your destination, the car stops, and you find the tank is dry – obviously a leak, since you can see drops dripping. How many gallons of gasoline have you lost? You have lost 2 gallons, or 50 miles' worth of driving.





6. Antique Lamps

   You bought 2 antique lamps for $50 each. Later, you were offered $60 for one and sold it. Then you changed your mind when you saw another such lamp being sold for more, and bought it back for $70. You then sold it for $80. The second one didn’t sell at all, so you reduced its price by 10% of what you paid for it and finally managed to get rid of it. When the saga of the lamps ended, did you make or lose money, and how much? You made $15.

7. Hours and Yards

   Are there more seconds in 100 hours or inches in 100 yards? Seconds in 100 hours. There are 360,000 seconds in 100 hours as opposed to 3600 inches in 100 yards.

8. Candy Packets

   The local candy store sold large packets of candy for 25 cents and small packets for 10 cents. The new cashier wasn’t up to the job, though; she marked down the number of sacks she sold, but forgot to record their prices. At the end of the day, she found she had sold 385 candy packs and had $62.65 in her cash register. Fortunately, she figured out how many of each size of candy packs she had sold before her boss came by. Can you? 161 large packs and 224 small ones.

9. Double Boiler

   You have one of those fancy double boilers whose lid fits either pot. They aren't very heavy pots, either. The bigger pot weighs 12 ounces by itself; with the lid on, it weighs twice as much as the little pot without the cover. The little pot, with the lid on, weighs one third-more than the big pot all by itself. What does the pot lid weigh by itself? 6 2/3 ounces

10. Hard Race

    Two children were running as hard as they could. They averaged 6 miles an hour, and then they had to rest. After resting, they only averaged 4 miles an hour on the way back. Not counting resting time, what was their average speed? 4.8, although many will answer 5. The answer is obtained by dividing the distance covered by the time elapsed. While the distance is not given, any distance will do. If you take a 12-mile run, it would take them 2 hours out and 3 hours back. They would then have covered 24 miles in 5 hours.