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How do I write 100 using all the digits from 1 to 9, not necessarily in their natural order, with only one written symbol which denotes an operation?
Also I wish to know how many ways are there to write statements which equals to 100 using all the digits in their natural order such as:
100=123-45-67=89
(pls list down the ways)
this is not homework, i saw this question on a maths magazine. Invisiblebug590 ( talk) 10:51, 12 January 2008 (UTC)
By the way, is there a prize in the magazine for solving this, and if you win it, will you share with Wikipedia? SpinningSpark 16:53, 12 January 2008 (UTC)
Say we have a raffle with 100 tickets and 3 prizes. One and one ticket is sold until all the prizes are won. How many tickets can you expect to sell?
I can find the answer in R with Monte Carlo simulation:
> a<-replicate(1e6,max(sample(100,3))) > mean(a) [1] 75.76514
And the pdf:
> table(a)/length(a) a 3 4 5 6 7 8 9 10 0.000009 0.000017 0.000031 0.000061 0.000095 0.000124 0.000173 0.000240 11 12 13 14 15 16 17 18 0.000271 0.000341 0.000415 0.000490 0.000592 0.000621 0.000702 0.000852 19 20 21 22 23 24 25 26 0.000935 0.001054 0.001223 0.001284 0.001379 0.001580 0.001800 0.001801 27 28 29 30 31 32 33 34 0.002051 0.002104 0.002342 0.002460 0.002743 0.002983 0.003021 0.003263 35 36 37 38 39 40 41 42 0.003510 0.003664 0.003782 0.004103 0.004300 0.004583 0.004832 0.005045 43 44 45 46 47 48 49 50 0.005392 0.005691 0.005824 0.006133 0.006435 0.006764 0.007052 0.007013 51 52 53 54 55 56 57 58 0.007601 0.007802 0.008294 0.008482 0.008876 0.009179 0.009520 0.009832 59 60 61 62 63 64 65 66 0.010120 0.010691 0.010846 0.011362 0.011675 0.012062 0.012457 0.012694 67 68 69 70 71 72 73 74 0.013018 0.013750 0.014184 0.014458 0.014838 0.015364 0.015773 0.016187 75 76 77 78 79 80 81 82 0.016798 0.017136 0.017520 0.018039 0.018802 0.019151 0.019553 0.020083 83 84 85 86 87 88 89 90 0.020735 0.021073 0.021243 0.022291 0.022502 0.023258 0.023667 0.024278 91 92 93 94 95 96 97 98 0.024394 0.025330 0.025982 0.026277 0.027101 0.027910 0.028286 0.028522 99 100 0.029578 0.030246
It would be fun to have the exact values, and a formula for m tickets and n prizes.
Any suggestions?
-- Δεζηθ ( talk) 14:45, 12 January 2008 (UTC)
Working from the back end, so to speak, the probability that the 100th ticket is NOT a prize is;
The probability that there is not a prize in the last two tickets;
and generally for r tickets from the end;
The expected number of tickets is the value of r making Pr closest to 0.5
SpinningSpark
17:49, 12 January 2008 (UTC)
A better strategy is to not announce the prizes till you have sold all the tickets.
SpinningSpark
17:52, 12 January 2008 (UTC)
Your collective kind indulgence sought in solving this question that's been bugging me- and everyone I've bored with it.
Imagine a piece of cake, a segment, of radius R and angle at the apex (a). There is icing along the sector of circumference C. The fact that I like this icing, but my friend doesn't, causes us to agree to cut the cake on a line perpendicular to R at half a. We wish to each have equal volumes of cake sponge- The cake is of even height. The icing cannot be scraped off, nor can the cake be cut at half the height (above the plate). These sneaky suggestions have already been put forward! If we cut the cake half way between the apex and the icing, then clearly I get too much cake in my (almost) trapezius and my friend gets too little in their triangle. How far up or down the R, at half a, should we cut the cake to ensure equal amounts of cake? The icing is neglible (though tasty). —Preceding unsigned comment added by Geoffgraves ( talk • contribs) 21:06, 12 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 11 | << Dec | January | Feb >> | January 13 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
How do I write 100 using all the digits from 1 to 9, not necessarily in their natural order, with only one written symbol which denotes an operation?
Also I wish to know how many ways are there to write statements which equals to 100 using all the digits in their natural order such as:
100=123-45-67=89
(pls list down the ways)
this is not homework, i saw this question on a maths magazine. Invisiblebug590 ( talk) 10:51, 12 January 2008 (UTC)
By the way, is there a prize in the magazine for solving this, and if you win it, will you share with Wikipedia? SpinningSpark 16:53, 12 January 2008 (UTC)
Say we have a raffle with 100 tickets and 3 prizes. One and one ticket is sold until all the prizes are won. How many tickets can you expect to sell?
I can find the answer in R with Monte Carlo simulation:
> a<-replicate(1e6,max(sample(100,3))) > mean(a) [1] 75.76514
And the pdf:
> table(a)/length(a) a 3 4 5 6 7 8 9 10 0.000009 0.000017 0.000031 0.000061 0.000095 0.000124 0.000173 0.000240 11 12 13 14 15 16 17 18 0.000271 0.000341 0.000415 0.000490 0.000592 0.000621 0.000702 0.000852 19 20 21 22 23 24 25 26 0.000935 0.001054 0.001223 0.001284 0.001379 0.001580 0.001800 0.001801 27 28 29 30 31 32 33 34 0.002051 0.002104 0.002342 0.002460 0.002743 0.002983 0.003021 0.003263 35 36 37 38 39 40 41 42 0.003510 0.003664 0.003782 0.004103 0.004300 0.004583 0.004832 0.005045 43 44 45 46 47 48 49 50 0.005392 0.005691 0.005824 0.006133 0.006435 0.006764 0.007052 0.007013 51 52 53 54 55 56 57 58 0.007601 0.007802 0.008294 0.008482 0.008876 0.009179 0.009520 0.009832 59 60 61 62 63 64 65 66 0.010120 0.010691 0.010846 0.011362 0.011675 0.012062 0.012457 0.012694 67 68 69 70 71 72 73 74 0.013018 0.013750 0.014184 0.014458 0.014838 0.015364 0.015773 0.016187 75 76 77 78 79 80 81 82 0.016798 0.017136 0.017520 0.018039 0.018802 0.019151 0.019553 0.020083 83 84 85 86 87 88 89 90 0.020735 0.021073 0.021243 0.022291 0.022502 0.023258 0.023667 0.024278 91 92 93 94 95 96 97 98 0.024394 0.025330 0.025982 0.026277 0.027101 0.027910 0.028286 0.028522 99 100 0.029578 0.030246
It would be fun to have the exact values, and a formula for m tickets and n prizes.
Any suggestions?
-- Δεζηθ ( talk) 14:45, 12 January 2008 (UTC)
Working from the back end, so to speak, the probability that the 100th ticket is NOT a prize is;
The probability that there is not a prize in the last two tickets;
and generally for r tickets from the end;
The expected number of tickets is the value of r making Pr closest to 0.5
SpinningSpark
17:49, 12 January 2008 (UTC)
A better strategy is to not announce the prizes till you have sold all the tickets.
SpinningSpark
17:52, 12 January 2008 (UTC)
Your collective kind indulgence sought in solving this question that's been bugging me- and everyone I've bored with it.
Imagine a piece of cake, a segment, of radius R and angle at the apex (a). There is icing along the sector of circumference C. The fact that I like this icing, but my friend doesn't, causes us to agree to cut the cake on a line perpendicular to R at half a. We wish to each have equal volumes of cake sponge- The cake is of even height. The icing cannot be scraped off, nor can the cake be cut at half the height (above the plate). These sneaky suggestions have already been put forward! If we cut the cake half way between the apex and the icing, then clearly I get too much cake in my (almost) trapezius and my friend gets too little in their triangle. How far up or down the R, at half a, should we cut the cake to ensure equal amounts of cake? The icing is neglible (though tasty). —Preceding unsigned comment added by Geoffgraves ( talk • contribs) 21:06, 12 January 2008 (UTC)