# A math riddle for you. Feel free to submit your own. **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [October 19, 2018, 12:15pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205 "2018-10-19T12:15:49Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [October 20, 2018, 2:01am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/41 "2018-10-20T02:01:40Z")
I’ll take my time going through the riddles/puzzles posted. I like to work it out for myself before reading the solution. I used to buy the math puzzle books. That was decades ago. I’ve slowed down since then. 😉 Many of the adult books require statistics and I never took that in college. I got a taste of it in Algebra II and knew statistics wasn’t where my talents lay. I’m better at working equations in Physics and electronics. ---
**Author:** ![Doug\_K](https://avatars.discourse-cdn.com/v4/letter/d/b5ac83/32.png) [@Doug\_K](https://boards.straightdope.com/u/Doug_K)\ **Post date:** [October 20, 2018, 4:23am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/42 "2018-10-20T04:23:47Z")
What’s the relationship between Salagadoola and Mechika Boola? Salagadoola + Mechika Boola + Bibbidi-bobbidi-boo = Bibbidi-bobbidi-boo. Subtract Bibbidi-bobbidi-boo from both sides: Salagadoola + Mechika Boola = 0 Subtract Mechika Boola from both sides: Salagadoola = -Mechika Boola ---
**Author:** ![UltraVires](https://avatars.discourse-cdn.com/v4/letter/u/ecccb3/32.png) [@UltraVires](https://boards.straightdope.com/u/UltraVires)\ **Post date:** [October 20, 2018, 5:33am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/43 "2018-10-20T05:33:38Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Here’s one that I came up with myself (well, took an extremely simple puzzle and complicated it): > > My first job was for a bottled tea company. We sold tea in cases of 100, and we sold three kinds of cases: sweet tea, unsweet tea, and assorted (50 each sweet and unsweet). The tea looked the same, only the labels were different. > > I was the delivery driver, and my first day, I had a case of each to deliver. Just as I was getting ready to leave, my boss got a call from the bottling factory. “We got a problem,” the bottle-labeler said. “I noticed that the labeling machine was broken, so none of the bottles got labels.” > > “Crap,” my boss said. “Okay, we’ll send them back. Put sweet labels on the ones in the sweet case, put unsweet labels on the one in the unsweet case, and I dunno, throw away the ones in the assorted case, no fixing that one.” > > “Uh, there’s another problem. I noticed that the case labeler mixed up the labels. There is definitely one case of each, but it put the wrong label on each case.” > > “Dammit. Which label went on which case?” > > “Uh, I forget?” > > My boss hung up. “Okay, first thing we do, we fire that guy, that guy is terrible. But now we’re gonna have to start tasting bottles of tea until we figure out which case has both sweet tea and unsweet tea in it, and then we’ll be able to figure things out, but who knows how many bottles we’ll have to go through and waste? This is a disaster!” > > “Actually,” I said, “I can fix it by tasting a single bottle: one sip, and I’ll tell you which label to put on which case. As a bonus, I can tell you how to salvage the case of assorted tea.” > > How did I do it? Point of clarification. Do we know absolutely that the case labels are wrong, or were they just randomly assigned such that the labels (one or more) may be accidentally correct? ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [October 20, 2018, 7:01am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/44 "2018-10-20T07:01:44Z")
> [@Doug\_K](#): > > What’s the relationship between Salagadoola and Mechika Boola? > > Salagadoola + Mechika Boola + Bibbidi-bobbidi-boo = Bibbidi-bobbidi-boo. > Subtract Bibbidi-bobbidi-boo from both sides: > Salagadoola + Mechika Boola = 0 > > Subtract Mechika Boola from both sides: > Salagadoola = -Mechika Boola Incorrect. [spoiler]You forgot that Salagadoola means Mechicka Boola. Therefore in addition to: Salagadoola + Mechika Boola + Bibbidi-bobbidi-boo = Bibbidi-bobbidi-boo You also know: Salagadoola = Mechika Boola Salagadoola and Mechicka Boola must both equal zero to make both equations correct.[/spoiler] ---
**Author:** ![vperry1](https://avatars.discourse-cdn.com/v4/letter/v/ee7513/32.png) [@vperry1](https://boards.straightdope.com/u/vperry1)\ **Post date:** [October 20, 2018, 7:13pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/45 "2018-10-20T19:13:10Z")
Not a math puzzle, but mathematically comical and true. My brother walked in to a pizza joint and ordered a pizza. The pizza cook took the pie from the oven and asked: Pizza cook: “Are you on a diet?” Brother: (slightly offended) “No. Why?” Pizza cook: “Well, if you were, I’d cut this into 6 slices instead of 8.” ---
**Author:** ![Malleus\_Incus\_Stapes](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/malleus_incus_stapes/32/3293_2.png) [@Malleus\_Incus\_Stapes](https://boards.straightdope.com/u/Malleus_Incus_Stapes)\ **Post date:** [October 21, 2018, 12:26am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/46 "2018-10-21T00:26:57Z")
> [@markn\_1](#): > > The way I’ve always heard this one is the final question is “how many stops did the bus make”? I’ve heard it as “What color is the bus driver’s eyes?” > [@](#): > > I think this is better because the answer similarly turns out to be much simpler than expected, but in this case the questionee won’t be able to give the right answer (assuming he was keeping track of the passengers rather than the stops). What you said is logical, but by the time the teller gets to the end of the riddle, I think most people have forgotten the wording at the beginning. (There’s a riddle that goes something like “Karen’s mother has four children: Penny, Nicholas, and Dime. What is the fourth child’s name?” Shorter than the bus one, but many people have already edited the “extraneous” opening details out of their minds by the time you’re done). (On that note, I think you guys should really lay off of **Acey**. People will very often say a stupid “obvious” answer because the way the question was asked short-circuits their brains). ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [October 21, 2018, 2:41pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/47 "2018-10-21T14:41:09Z")
Before each game of the upcoming World Series, the Dodgers and Red Sox will engage in competitive coin flipping. Each team will gather and at a signal each manager will flip a quarter and record the results. They will then again flip their quarters and record the results. Each team’s manager will continue simultaneously to flip their coins until one team wins the day’s competition. The Dodgers will win if at some point they flip a head and next a tail. The Red Sox will win if they at some point flip a head and then next a head. If the two teams win at the same time the result is a tie. If there is a tie results are scrapped and the day’s flipping competition must start over. Each day you have the opportunity to bet on either the Dodgers or Red Sox to win the coin flip competition. Which team do you choose? ---
**Author:** ![Lucas\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lucas_jackson/32/303_2.png) [@Lucas\_Jackson](https://boards.straightdope.com/u/Lucas_Jackson)\ **Post date:** [October 21, 2018, 3:38pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/48 "2018-10-21T15:38:07Z")
> [@Hari\_Seldon](#): > > Here is one that’s a bit harder. You core an apple and the cored apple that remains is 4 inches high. What is its volume (the cored apple). Assume the apple started out as a perfect sphere. > > You could do this using calculus (I have checked the answer that way), but if you simply assume that there is an answer independent of the original size of the apple, you conclude that it must be the same if the core is 0 and the apple was originally 4" high. In that case its radius is 2" and its volume is 4_pi_r^3/3 = 32\*pi/3 Some of these aren’t riddles in the sense of the OP, they are just math problems. ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [October 21, 2018, 3:52pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/49 "2018-10-21T15:52:30Z")
> [@Lucas\_Jackson](#): > > Some of these aren’t riddles in the sense of the OP, they are just math problems. True, but a good math puzzle riddle (i.e. Monty Hall) will often have an “easy” answer that turns out to be wrong because of… _math_. Other riddles the math is straightforward, but the wording of the riddle is the trick. Both qualify as math riddles to me. ---
**Author:** ![Dickerman](https://avatars.discourse-cdn.com/v4/letter/d/8baadc/32.png) [@Dickerman](https://boards.straightdope.com/u/Dickerman)\ **Post date:** [October 21, 2018, 4:04pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/50 "2018-10-21T16:04:24Z")
For the OP, the correct answer is the younger brother is almost certainly dead. ---
**Author:** ![Ulf\_the\_Unwashed](https://avatars.discourse-cdn.com/v4/letter/u/b4bc9f/32.png) [@Ulf\_the\_Unwashed](https://boards.straightdope.com/u/Ulf_the_Unwashed)\ **Post date:** [October 21, 2018, 5:40pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/51 "2018-10-21T17:40:27Z")
> [@aceplace57](#): > > I’ll start with a classic math riddle. Please Submit your own favorites. > > If your friend’s son is four years old and his little brother is half his age (two years old), how old will the younger brother be if the older brother is 100?’ > > 98. The “half his age” is a red herring and useless information. Many people will insist the younger brother is 50. In the original editions of the Bobbsey Twins books, the older twins (Bert and Nan) were eight and the younger ones,Freddie and Flossie, were four. When the publisher decided to appeal to a somewhat older audience in the sixties (?) the older twins became twelve and the younger set…six. If my friend is Mr or Mrs. Bobbsey, and who is to say otherwise?, then the answer IS 50. ---
**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\ **Post date:** [October 21, 2018, 5:53pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/52 "2018-10-21T17:53:34Z")
> [@Biotop](#): > > Before each game of the upcoming World Series, the Dodgers and Red Sox will engage in competitive coin flipping. Each team will gather and at a signal each manager will flip a quarter and record the results. They will then again flip their quarters and record the results. Each team’s manager will continue simultaneously to flip their coins until one team wins the day’s competition. > > The Dodgers will win if at some point they flip a head and next a tail. The Red Sox will win if they at some point flip a head and then next a head. If the two teams win at the same time the result is a tie. If there is a tie results are scrapped and the day’s flipping competition must start over. > > Each day you have the opportunity to bet on either the Dodgers or Red Sox to win the coin flip competition. Which team do you choose? After the first head, the Red Sox will have a 50% chance to win on all further tosses, by contrast the Dodgers will have to go back to the beginning on each miss. If they were both using the same coin it would be 50/50 but tossing seperately works out better for the Red Sox. ---
**Author:** ![K364](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k364/32/5_2.png) [@K364](https://boards.straightdope.com/u/K364)\ **Post date:** [October 21, 2018, 7:37pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/53 "2018-10-21T19:37:20Z")
Mr Shine, I don’t get that. I think you meant the other way around. Another way of wording is: a miss by the Dodgers would be a head, and they have a chance of winning on the next toss. A miss by the Red Sox would be a tail and they cannot win on the next toss, they have to start over waiting for a head to start the HT winning sequence. I ran a simulation and found the Dodgers win around 62.5 % ---
**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\ **Post date:** [October 21, 2018, 7:45pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/54 "2018-10-21T19:45:13Z")
> [@K364](#): > > Mr Shine, I don’t get that. I think you meant the other way around. Yes I mixed the teams up :smack: ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [October 21, 2018, 8:33pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/55 "2018-10-21T20:33:33Z")
> [@iamthewalrus\_3](#): > > One of my favorite math puzzlers is with a standard 5-card hand from a standard 52-card deck. > > One player looks at the 5 cards, removes one card face down. Passes a pile of the other 4 cards to the second player. The second player looks at the 4 cards and names the face-down card he hasn’t seen. The two players are allowed to come up with a strategy before playing, but they don’t know which 5 cards are in the hand. > > How do you do it? This is an old classic. My son and I once practiced a simple technique to do this and dazzle a spectator. (Unfortunately, my son no longer has time for games with his old man. :o ) No verbal or manual clues are allowed. All you’re allowed is to select one of 4! orderings for the four cards you retain. Since 4! = 24 \< (52-4) this may seem not enough, but it is. In fact, you can work a sure-guess with a deck of 124 instead of just 52! … But the details are much harder. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [October 21, 2018, 8:45pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/56 "2018-10-21T20:45:54Z")
I started a thread 8 years ago about one of my favorite math puzzles: _A duck swims in a perfectly circular pond. There is a fox at the shore, afraid of water, that plans to catch the duck when getting out. The land speed of the fox is 4.6 times as high as the water speed of the duck. However, once the duck reaches the shore without the fox in its immediate neighborhood, it can hide and escape. Starting from the center, can the duck reach the shore safely?_ This puzzle is a well-known Microsoft interview puzzle or such, IIRC, _ **but with the fox’s speed advantage only 4 instead of 4.6** _. WARNING: With 4.6 substituted for 4, the puzzle, even without trying to formulate rigorous proof, seems to be difficult. ---
**Author:** ![K364](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k364/32/5_2.png) [@K364](https://boards.straightdope.com/u/K364)\ **Post date:** [October 21, 2018, 8:56pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/57 "2018-10-21T20:56:45Z")
> [@septimus](#): > > This is an old classic. My son and I once practiced a simple technique to do this and dazzle a spectator. (Unfortunately, my son no longer has time for games with his old man. :o ) > > No verbal or manual clues are allowed. All you’re allowed is to select one of 4! orderings for the four cards you retain. Since 4! = 24 \< (52-4) this may seem not enough, but it is. > > In fact, you can work a sure-guess with a deck of 124 instead of just 52! … But the details are much harder. Hmmm… there’s no restriction on how the deck is handed back, so face-up, face-down is 16 more combinations, and head tilted to left or right or not tilted, leaning forward or back or not leaning, one eye closed… etc, etc. So, I think can be done with a deck of a million or more. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [October 21, 2018, 9:49pm UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/58 "2018-10-21T21:49:31Z")
> [@K364](#): > > Hmmm… there’s no restriction on how the deck is handed back, so face-up, face-down is 16 more combinations, and head tilted to left or right or not tilted, leaning forward or back or not leaning, one eye closed… etc, etc. > > So, I think can be done with a deck of a million or more. Yes, it’s difficult to word the puzzle to outlaw various signals. _But the intent of the puzzle_ is that you have nothing to go on but the ordering of the 4 cards. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [October 22, 2018, 12:21am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/59 "2018-10-22T00:21:28Z")
> [@UltraVires](#): > > Point of clarification. Do we know absolutely that the case labels are wrong, or were they just randomly assigned such that the labels (one or more) may be accidentally correct? > [@Left\_Hand\_of\_Dorkness](#): > > I was the delivery driver, and my first day, I had a case of each to deliver. > … > “Uh, there’s another problem. I noticed that the case labeler mixed up the labels. There is definitely one case of each, but it put the wrong label on each case.” (emphasis added). Those lines were there to make this as clear as possible. Mr. Shine and iamthewalrus between them got the primary solution and bonus problems right :). Yeah, it’s a gussied-up classic problem, but I like my version a lot more than the usual “black and white balls in boxes” formulation. ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [October 22, 2018, 4:17am UTC](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205/60 "2018-10-22T04:17:24Z")
> [@septimus](#): > > I started a thread 8 years ago about one of my favorite math puzzles: > _A duck swims in a perfectly circular pond. There is a fox at the shore, afraid of water, that plans to catch the duck when getting out. The land speed of the fox is 4.6 times as high as the water speed of the duck. However, once the duck reaches the shore without the fox in its immediate neighborhood, it can hide and escape. Starting from the center, can the duck reach the shore safely?_ > This puzzle is a well-known Microsoft interview puzzle or such, IIRC, _ **but with the fox’s speed advantage only 4 instead of 4.6** _. > WARNING: With 4.6 substituted for 4, the puzzle, even without trying to formulate rigorous proof, seems to be difficult. Can the duck simply fly out of the lake? [Previous page](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205.md?page=2) [Next page](https://boards.straightdope.com/t/a-math-riddle-for-you-feel-free-to-submit-your-own/823205.md?page=4)