Indyra Posted October 28, 2009 Report Share Posted October 28, 2009 A problem was given to me by a 5th grade child i found it very interesting so who ever solves it out first gets a WP So here it is and good luck A 4 digit number divided by its inverted self equlas 6 and rest 933 Find the number knowing that the difference between the first digit and the last equals 7 and the difference between the 2nd and 3rd digit equals 2. There are 2 ways of solving this so there will be 2 WP as reward for those who give out the correct and full mathematical explanation. Link to comment Share on other sites More sharing options...
Indyra Posted October 28, 2009 Author Report Share Posted October 28, 2009 And we have the first winner : Shadowseeker I'll post his method after the quest ends Link to comment Share on other sites More sharing options...
Malaikat Maut Posted October 28, 2009 Report Share Posted October 28, 2009 What do you mean it equals "6 and rest 933"? Link to comment Share on other sites More sharing options...
Indyra Posted October 28, 2009 Author Report Share Posted October 28, 2009 (edited) [quote name='Malaikat Maut' date='28 October 2009 - 08:45 PM' timestamp='1256762723' post='45980'] What do you mean it equals "6 and rest 933"? [/quote] The number doesn't divide perfectly ..it has a rest P.s the deduction method was found by Shadow . still waiting for the 2nd method Edited October 28, 2009 by Indyra Link to comment Share on other sites More sharing options...
Indyra Posted October 28, 2009 Author Report Share Posted October 28, 2009 2nd winner Kafuuka ( but he found a 3rd way of solving it very similar to what i;m looking for) so there will be a 3rd WP for the one who solves it exactly my way Link to comment Share on other sites More sharing options...
Kafuuka Posted October 28, 2009 Report Share Posted October 28, 2009 [quote name='Indyra' date='28 October 2009 - 09:12 PM' timestamp='1256760774' post='45975'] A 4 digit number divided by its inverted self equlas 6 and rest 933 [/quote] I think you meant divided by it's mirror. The inverse of x is 1/x (in most contexts) and dividing x by it's inverse is equal to squaring x, which obviously wouldn't make sense in the context. Link to comment Share on other sites More sharing options...
awiiya Posted October 28, 2009 Report Share Posted October 28, 2009 Yes, I found your wording a little bit confusing. Awi Link to comment Share on other sites More sharing options...
Indyra Posted October 28, 2009 Author Report Share Posted October 28, 2009 (edited) After reading your answers i just figured the there is no 3rd way of solving this because the 2nd and 3rd methods are almost identically So the quest has now ended : the winner are Shadow seeker and Kafuuka The solutions were Shadow Seeker We know 6x+933=Y And that if we write the number as WYXZ that W-Z=7 Since it is 6 times higher that the reverse, Z has to be 1 and W 8 Otherwise the equation would make no sense. We're dealing with numbers out of N, so only these work, although theoretically 7 and 0 work as well. The issue with 6x (lower than 1k)+ lower than 1 k is that it won't reach 7 k, so we know it's 8 and 1, since 2 *6 isn't anywhere close to 9 and exceeding the limits. The next step is the missing two numbers from the mid, all you need is just a little testing with the numbers you input 97, 86, etc and go down using a calculator: everything that divided by it's reverse gets 6 is marked and then you just check which is the right one. Solution: 8421 and Kafuuka's a * 1000 + b * 100 * c * 10 + d - 933 = 6* ( a + b *10 + c *100 + d *1000 ) |a - d|= 7 |b - c|= 2 994 a + 40 b - 590 c - 5999 d = 933 from this we can guess a should be larger then d, thus a = d + 7 trying b = c +2 or c - 2: 994 ( d +7) + 40 ( c +? 2) - 590 c - 5999 d = 933 - 5005 d - 550 c = - 6105 +160? d = 1 c = 2 a = 8 b = 4 8421 - 933 / 1248 = 6 Edited October 28, 2009 by Indyra Link to comment Share on other sites More sharing options...
tankfans Posted October 29, 2009 Report Share Posted October 29, 2009 I just found our the quest.... If only the quest had last for at least a day... Link to comment Share on other sites More sharing options...
AqlBeast Posted October 29, 2009 Report Share Posted October 29, 2009 -__- Finally ace my Cal II test and here I am...late for this math problem. What luck? Kakkaka Link to comment Share on other sites More sharing options...
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