# Someone please tell me how this 7 Up number puzzle thingy works **URL:** \ **Category:** Factual Questions\ **Created:** [August 16, 2003, 6:37am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551 "2003-08-16T06:37:22Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![Marlitharn](https://avatars.discourse-cdn.com/v4/letter/m/779978/32.png) [@Marlitharn](https://boards.straightdope.com/u/Marlitharn)\ **Post date:** [August 16, 2003, 6:37am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/1 "2003-08-16T06:37:22Z")
Okay, I know [this](http://digicc.com/fido/) probably has a perfectly simple and logical mathematical answer, but I’ve always been lousy at figuring out number puzzles. My co-workers are no better (one co-worker, in fact, hid her paper from the screen, so the little 7 Up guy couldn’t peek at it). So can someone smarter than me tell me how this thing works? ---
**Author:** ![GuanoLad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guanolad/32/42_2.png) [@GuanoLad](https://boards.straightdope.com/u/GuanoLad)\ **Post date:** [August 16, 2003, 6:46am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/2 "2003-08-16T06:46:14Z")
My guess is it has something to do with the magic number 9. But I still can’t see how. Boy, that’s a clever maths trick! ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [August 16, 2003, 6:52am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/3 "2003-08-16T06:52:28Z")
Groovey ---
**Author:** ![Stage\_Manager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/stage_manager/32/7267_2.png) [@Stage\_Manager](https://boards.straightdope.com/u/Stage_Manager)\ **Post date:** [August 16, 2003, 7:02am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/4 "2003-08-16T07:02:02Z")
How’s your algebra? You’ll need it for [this site](http://www.rain.org/~mkummel/stumpers/27oct00a.html), which explains it pretty well, I think. ---
**Author:** ![Marley23](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Marley23](https://boards.straightdope.com/u/Marley23)\ **Post date:** [August 16, 2003, 7:25am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/5 "2003-08-16T07:25:24Z")
Yeah, it’s all done with 9s. 🙂 Just like that Crystal Ball site that had everybody on boards other than this one so puzzled. 😉 ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [August 16, 2003, 7:26am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/6 "2003-08-16T07:26:47Z")
Do you remembe the test for divisiblity by 9? You sum the digits. Then sum the digits of the result until you have a single digit. If the result is 9, the number is divisible by 9. If the result is not 9, then the result is the remainder you get if you divide the original number by 9. Rearanging the digits does not change the remainder. Let r be the remainder. The original number is 9k[sub]1[/sub] + r, for some k[sub]1[/sub]. When you rearange the digits, the number is going to be 9k[sub]2[/sub], for some k[sub]2[/sub]. The difference is 9(k[sub]1[/sub] - k[sub]2[/sub]) (or its negative). Since we have a multiple of 9 now, we know that the sum of the digits of the difference must be 9. We can use this to find the missing digit. Sum the remaining digits until you have a single digit. If you get 9, the missing digit must be 9. If the sum is not 9, subtract the result from 9 and you will have the missing digit. The reason they asked you not to circle a zero is this process cannot distinguish a zero from a nine. ---
**Author:** ![Marlitharn](https://avatars.discourse-cdn.com/v4/letter/m/779978/32.png) [@Marlitharn](https://boards.straightdope.com/u/Marlitharn)\ **Post date:** [August 16, 2003, 7:35am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/7 "2003-08-16T07:35:42Z")
I figured it probably had something to do with 9s, but I’m still not clear on how this one works. **Mikie** ’s site is kind of sort of penetrating the fog, but it’s the random bit at the end where it has you circle a number and then shows you the number you circled that has me confused. What kills me is the answer is probably staring me right in the face and I’ll have to hit myself in the head and say, “D’oh!” as soon as someone points it out to me. My defense is I’m on Darvocet for back pain. _preview_ _reads **DrMatrix’s** explanation_ D’oh! :smack: Thanks, guys! ---
**Author:** ![Robot\_Arm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robot_arm/32/18280_2.png) [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)\ **Post date:** [August 16, 2003, 7:38am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/8 "2003-08-16T07:38:43Z")
I love the instruction to “make it completely random, with lots of different digits.” Very sneaky. A completely random number might have all the same digits, but if you did that, then rearrange the digits and subtract, you’d get 0 and the trick wouldn’t work. ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [August 16, 2003, 8:12am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/9 "2003-08-16T08:12:50Z")
> [@](#): > > \*Originally posted by \*\*\*DrMatrix \*\* > > When you rearange the digits, the number is going to be 9k[sub]2[/sub], for some k[sub]2[/sub]. The above should be: When you rearange the digits, the number is going to be 9k[sub]2[/sub] + r, for some k[sub]2[/sub]. ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [August 17, 2003, 5:12am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/10 "2003-08-17T05:12:56Z")
> [@](#): > > \*Originally posted by DrMatrix \* > \*\*The above should be: > When you rearange the digits, the number is going to be 9k[sub]2[/sub] + r, for some k[sub]2[/sub]. \*\* Sorry for this slight hijack. It says Moderator under your name, so doesn’t that mean you “…generally have the ability to edit and delete posts…” (direct quote from the board’s faq) including your own? Or is that “generally” implying that only _some_ mods can do that? ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [August 17, 2003, 5:56am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/11 "2003-08-17T05:56:20Z")
Perhaps Moderators are discouraged from using their powers to just fix typos ad things. ---
**Author:** ![xash](https://avatars.discourse-cdn.com/v4/letter/x/c6cbf5/32.png) [@xash](https://boards.straightdope.com/u/xash)\ **Post date:** [August 17, 2003, 10:15am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/12 "2003-08-17T10:15:19Z")
The puzzle doesn’t work if you choose 666 as your starting number. I guess the devil is in the details. ---
**Author:** ![GuanoLad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guanolad/32/42_2.png) [@GuanoLad](https://boards.straightdope.com/u/GuanoLad)\ **Post date:** [August 17, 2003, 11:33am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/13 "2003-08-17T11:33:49Z")
They ask for different numbers. You can’t subtract the same number from itself, that just wouldn’t work. ---
**Author:** ![MarkyDeSade](https://avatars.discourse-cdn.com/v4/letter/m/35a633/32.png) [@MarkyDeSade](https://boards.straightdope.com/u/MarkyDeSade)\ **Post date:** [August 17, 2003, 11:51am UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/14 "2003-08-17T11:51:44Z")
It didn’t work with 1111 either (my first try). Oh. I see you’ve alteady noticed that. I’m posting anyway. It’s been a while. ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [August 17, 2003, 2:03pm UTC](https://boards.straightdope.com/t/someone-please-tell-me-how-this-7-up-number-puzzle-thingy-works/195551/15 "2003-08-17T14:03:22Z")
> [@](#): > > \*Originally posted by \*\*\*TJdude825 \*\* > Sorry for this slight hijack. It says Moderator under your name, so doesn’t that mean you “…generally have the ability to edit and delete posts…” (direct quote from the board’s faq) including your own? Or is that “generally” implying that only _some_ mods can do that? I could have edited my post for the correction, but I was posting as a member, not as a moderator. Since members cannot edit their posts, it’s not really fair for me to edit my posts when I’m posting as a member. There is no official rule about this, and if I’d noticed the mistake right away, I might have edited it for the correction (and corrected my mis-spelling of remember).