# Bulls and Cows **URL:** \ **Category:** Thread Games\ **Created:** [August 8, 2020, 5:39am UTC](https://boards.straightdope.com/t/bulls-and-cows/917561 "2020-08-08T05:39:49Z")\ **Posts on this page:** 20\ **Page:** 5
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 3:20pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/81 "2020-08-10T15:20:33Z")
Interesting choice. 0864 has no bulls and one cow. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 10, 2020, 3:21pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/82 "2020-08-10T15:21:03Z")
Next, 5321. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 3:22pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/83 "2020-08-10T15:22:27Z")
5321 has one bull and one cow. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 10, 2020, 3:24pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/84 "2020-08-10T15:24:19Z")
7986, so that we can see how we stand. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 3:25pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/85 "2020-08-10T15:25:25Z")
7986 has no bulls and one cow. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | | 3 | 7986 | 0 | 1 | ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 10, 2020, 3:34pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/86 "2020-08-10T15:34:11Z")
1. 🙂 ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 3:36pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/87 "2020-08-10T15:36:51Z")
4790 has two bulls and no cows. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | | 3 | 7986 | 0 | 1 | | 4 | 4790 | 2 | 0 | ---
**Author:** ![Prof.Pepperwinkle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/prof.pepperwinkle/32/13627_2.png) [@Prof.Pepperwinkle](https://boards.straightdope.com/u/Prof.Pepperwinkle)\ **Post date:** [August 10, 2020, 3:58pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/88 "2020-08-10T15:58:46Z")
1. ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 10, 2020, 4:20pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/89 "2020-08-10T16:20:52Z")
8 and 6 are not included in the secret number because the fourth digit is either 7 or 9 and the number that includes both 7 and 9 has produced only 1 cow (all the other three digits being included in the two previous numbers, that is 0864 and 5321). Point A. We can say the first digit we know in the secret number is either 7 or 9 (because 8 and 6 are not included in the secret number). Point B. We can say the second digit we know in the secret number is either 0 or 4 (because 8 and 6 are not included in the secret number). Point C. The third and fourth digits two of the four included in the second number I guessed: 5321. Prof.Pepeerwinkle’s number may produce 2 bulls if 5 is the bull in the second number I guessed and if the second digit I mentioned in Point B is 0, (and 0’s position is not the third or fourth place in the secret number). The remaining matches that Prof.Pepperwinkle’s number can produce are 1 bull and 1 cow, 2 cows, or 1 cow (for reasons that I won’t elaborate). Prof.Pepperwinkle’s number will not produce 3 bulls, 4 bulls, or 0 bulls & 0 cows. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 4:40pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/90 "2020-08-10T16:40:10Z")
5064 has no bulls and one cow. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | | 3 | 7986 | 0 | 1 | | 4 | 4790 | 2 | 0 | | 5 | 5064 | 0 | 1 | ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 10, 2020, 4:51pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/91 "2020-08-10T16:51:30Z")
Let’s try 4723. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 4:53pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/92 "2020-08-10T16:53:20Z")
4723 has no bulls and two cows. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | | 3 | 7986 | 0 | 1 | | 4 | 4790 | 2 | 0 | | 5 | 5064 | 0 | 1 | | 6 | 4723 | 0 | 2 | ---
**Author:** ![Prof.Pepperwinkle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/prof.pepperwinkle/32/13627_2.png) [@Prof.Pepperwinkle](https://boards.straightdope.com/u/Prof.Pepperwinkle)\ **Post date:** [August 10, 2020, 4:57pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/93 "2020-08-10T16:57:27Z")
3590? ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 10, 2020, 4:58pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/94 "2020-08-10T16:58:52Z")
Getting closer. 3590 has two bulls and one cow. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | | 3 | 7986 | 0 | 1 | | 4 | 4790 | 2 | 0 | | 5 | 5064 | 0 | 1 | | 6 | 4723 | 0 | 2 | | 7 | 3590 | 2 | 1 | ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 11, 2020, 3:27am UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/95 "2020-08-11T03:27:04Z")
If my calculations are right, there is enough information already presented to narrow the choice down to one. ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 11, 2020, 4:05am UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/96 "2020-08-11T04:05:22Z")
> [@bibliophage](#): > > If my calculations are right I don’t doubt your calculations are right. It is a pity the game doesn’t attract more players. There are few views and much fewer participants. ---
**Author:** ![Monty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/monty/32/47_2.png) [@Monty](https://boards.straightdope.com/u/Monty)\ **Post date:** [August 11, 2020, 10:42am UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/97 "2020-08-11T10:42:33Z")
> [@PlaceboTarget](#): > > It is a pity the game doesn’t attract more players. There are few views and much fewer participants. Yep. And thanks for starting this thread; I’m finding it absolutely fascinating. ---
**Author:** ![Aspidistra](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aspidistra/32/3894_2.png) [@Aspidistra](https://boards.straightdope.com/u/Aspidistra)\ **Post date:** [August 11, 2020, 10:47am UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/98 "2020-08-11T10:47:56Z")
2390? ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [August 11, 2020, 1:56pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/99 "2020-08-11T13:56:18Z")
Ding-ding-ding-ding! We have a winner. Congratulations, Aspidistra. Now you’re the game master for the next round. | # | guess | Bulls | Cows | | --- | --- | --- | --- | | 1 | 0864 | 0 | 1 | | 2 | 5321 | 1 | 1 | | 3 | 7986 | 0 | 1 | | 4 | 4790 | 2 | 0 | | 5 | 5064 | 0 | 1 | | 6 | 4723 | 0 | 2 | | 7 | 3590 | 2 | 1 | | 8 | 2390 | 4 | 0 | ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [August 11, 2020, 2:01pm UTC](https://boards.straightdope.com/t/bulls-and-cows/917561/100 "2020-08-11T14:01:31Z")
Congratulations @Aspidistra ! [Previous page](https://boards.straightdope.com/t/bulls-and-cows/917561.md?page=4) [Next page](https://boards.straightdope.com/t/bulls-and-cows/917561.md?page=6)