_ _ _._ _\nPLEASE READ CAREFULLY\n1.The digit in the tens place is twice as big as the digit in the tenTHS place.\n2. The digit in the ones place is 1/2 the digit in the tenTHS place.\n3.The digit in the hundreTHS place is 1/2 the digit in the ones place.\n4. The digit in the hundreds place is the largest odd digit.\nPlease be correct
207139
Okay, the largest odd digit is nine, so you know the first one has to be nine, as the first blank is in the hundreds place.  \n\n--> 9 _ _ . _ _\n\nNo you must choose digits for the rest of the numbers so that the digit in the ones place is both twice as big as the digit in the hundreths places, and half as big as the digit in the tenths place.  But also, the digit in the tens place must be twice as big as the digit in te tenths place, so what you have here is:\n\ntens place digit = twice the tenths place digit \n\ntenths place digit = twice the ones place digit \n\nones place digit = twice the hundreths place digit.\n\nSo you can see that the larger of the remaining digit has got to be the tens place digit, and also, that the tens place digit has to be even (as well as the other digits save possibly the hundreths place one).  So, without getting into algebra or anything like that, you just pick a good large even digit for the tens place digit.  We'll go with 8, the largest even digit.  We see that:\n\n8/2 = 4 --> tenths place digit is 4.\n\n4/2 = 2 --> ones place digit is 2.\n\n2/2 = 1 --> hundreths place digit is one.\n\nThese satisfy all of the requirements, so your final number is:\n\n982.41\n\nHope that helps.
137737
Could be 10,14,13. The odd terms differ by 3 (eg. 4-1,7-4), the even terms differ by 4.
298050
A B C D E * 4 = E D C B A\nA can be 1 or 2, larger numbers would turn the multiplication into a 6 digit number. But the result ends with A, so A has to be even (any digit multiplied by 4 gives an even number) => A = 2.\nE is at least 4 * A = 8, so E = 8 or E = 9. But we also know that 4 * E results in a number ending with 2 (A), so E = 3 or E = 8. Combining these two gives E = 8.\n2 B C D 8 * 4 = 8 D C B 2\nNow we can do the same for the rest.\nSince there was no carry-over to the first digit, 4 * B < 10 => B <= 2\nWe also know that B has to be odd, because 4 * D gives an even number and there is a carry-over from 3 (4 * 8 = 32), so B = 1.\nB is also the last digit of the result of 4 * D + 3, so 4 * D has to end with 8, so D = 2 or D = 7. Since A = 2, D has to be 7.\n2 1 C 7 8 * 4 = 8 7 C 1 2\nWe now know that 4 * C + 3 = 30 + C => 3 * C = 27 => C = 9\n\nA B C D E = 2 1 9 7 8
123220
such a no. cannot exist but hey dude a great question lets look at it this way\nthe last digit of the given no. will be 6\nand the resulting no will be 4 times that no\nlast digit of 4*6 is 4 so the resulting nos last digit digit has to 4 \nthat would mean the first digit of the original no will  be 4\nso just as an eg let us consider the no. 46\n46*4 will be 184\nthat is the first digit will be 1(or 2 or 3 or 4 but never 6)\nthis will be followed by every no \nso u c such a no just canno exist
394271
This is solvable, and you wrote it very well!\n\nThe key to setting this up is knowing that for any 2-digit number, you can write it as 10a + b.\n\nSo your problem states that a+b=9 (the sum of the tens digit and ones digit is 9), and it states that a=3b+1 (the tens digit is 1 more than 3 times the ones digit).\n\nSo now you have 2 equations in 2 unknowns, which you can easily solve for:\n\na + b = 9\na = 3b + 1\n\nSubstitute a = 3b + 1 into the first equation to get:\n\na + b = 9\n(3b + 1) + b = 9\n4b + 1 = 9\n4b = 8\nb = 2\n\nNow you can easily solve for a, which equals 7 since a+b=9.\n\nSo your 2-digit number is 72.\n\nCheck: 7+2=9\n7 = 1 + 3*2\n\nIt checks out, so our answer is correct!\n\n~ ♥ ~
439972
a) 4 is in the tens place, so it is worth 4 * 10 = 40\nb) 6 is in the ones place, so it is worth 6 * 1 = 6\nc) 3 is in the thousands place, so it is worth 3 * 1000 = 3000\nd) first 2 is in the hundreds place, so it is worth 2 * 100 = 200\ne) 7 is in the hundreds place, so it is worth 7 * 100 = 700\n\nOr you can just say the numbers and see what you say when you are on the underlined number...\n\n42 = "forty two" so 4 is "forty"\n176 = "one hundred seventy six" so 6 is "six"\n3049 = "three thousand forty nine" so 3 is "three thousand"\n1223 = "one thousand two hundred twenty three" so first 2 is "two hundred"\n10731 = "ten thousand seven hundred thirty one" so 7 is "seven hundred"
447474
I think your teacher is pulling your leg. Pi is a non-terminating decimal. It doesn't have a "last digit" that is currently known.\n\nMany calculations of pi have been taken out to very large numbers of places. But saying that those calculations have been taken out to some particular place is not the same as saying that that value is the value of the *last* digit.\n\nJust the last one that has been calculated.\n\nSorry!
117717
This is 194. For this question, you have to know that 9 is the highest number, and for a difference of 8 to occur for digits it has to be 9-1 = 8, since no other numbers can satisfy this, then the tens digit is 9 and the hundred unit is 1 and then of course the ones digit is 5 less than  the tens unit that is 9-5 = 4 thus the number is 194
481280
let t be the tens digit and o be the ones digit\n\nt + o = 12\nt = o + 2\n\nsubstitute\n\n(o + 2) + o = 12\n\ngather like terms\n\n2o = 10\n\ndivide by 2\n\no = 5\n\nsubstitute this value into the equation t = o + 2\n\nt = (5) + 2\n\nt = 7\n\nSince t = 7 and o = 5, 75 is the correct answer good work!
218951
The first three digits are actually multiplied by (80 x 250) = 20000. And you are adding 250 which you have subtracted latter.\n\nIn effect two times the first three digits followed by four zeros. You are adding two times the four digits so you get two times the original number. Dividing it by 2 u get the original value.\n\nYou can do this with 40 and 500, 20 and 1000, 10 and 2000 etc.
240343
Let the units digit, tens digit and the hundreds digit be c,b and a respectively.\n\n       Now, the number is 100a+10b+c.\n\nGiven :  1. a+b+c = 9\n         2. b = 1/2(a+c)\n         3. a = 1/2(c)\n\nSolution :\n\n         Since, a = 1/2c\n                c = 2a  ..................I\n\n         Since  b = 1/2(a+c)\n              a+c = 2b  ..................II\n\n      As a+b+c = 9,\n          2b+b = 9   ........fromII\n            3b =9\n\n           b = 3.            \n\n From I and II,\n           2b = a+c = a+2a =3a\n\n           3a = 2*3 = 6\n            \n            a = 2\n\n From I,    c = 2a = 2*2 = 4\n\n     Hence the number is :\n\n          100a+10b+c = 100*2 + 10*3 + 4\n                     = 200 +30+4\n                     = 234\n\n The number is therefore 234.....ANSWER
365955
The original number is 82\n\nIf the tens digit is 4 times the unit digit then the only numbers that satisfy this condition are 82 and 41.\n\nTurning them round gives 28 and 14.\n\nOnly 28 satisfies the condition that the new number is 54 less than the original number.
659996
How does this work?  Is it okay to have a decimal in the middle?\n\nType 1   (Screen says 1)\n/ 3          (Screen says 0.3333333)\nx 3         (Screen says 0.9999999)\n+ 9        (Screen says 9.9999999)\n\n- Jack
69777
I can get you started. \n\nThe digit A can't be very large if ABCD * 4 is a 4 digit number. In fact 4  3 = 12 so if A = 3 then ABCD x 4 is at least five digits. \n\nA is either 1 or 2. If A is 1 then 1BCD x 4 = DCB1 But this is not possible since the left side is even and the right side is odd. Thus A = 2. \n\nso, we have the first number!\n\n2BCD x 4 = DCB2 \n\nLook at D on the right side. What can it be? 4 x 2 = 8 so D might be 8 or, if there is a carry, D might be 9. But if D on the left side is 9 we get 4 x 9 = 36 which doesn't work with the units digit of 2 on the right side. So, D = 8 and we get:\n\n2BC8 x 4 = 8CB2 \n\nThis should be enough to get you started
287293
this is possible to figure out.  What it is a combination of numbers   i will do examples to keep it simple.   If your number was 00  or 000  then the answer was 9.  well its a pattern    if your number is 001 then the answer he came up with was 8.  well then if you had 002  then it was 7.  but also on the note if your number was 011 or some combination of this number then it was 8 also  because when you take 011 and add 0+1+1 you get 2 so it was 8.   the way it works is the numbers you type in it adds them together so there is a correlating number that goes with the answer that was added together.  so... if the numer added together was 0 then it was 9.  and the number added together was 1 then he came up with 8.  added together you got 2 then he said 7.  and just keep going ... 3 is 6,   4 is 5.    also on the same account    5 is 4,  6 is 3,   7 is 2,   8 is 1,  and 9 is 0.
640634
N = 285714 and 1.5*N = 428571\n\nHere's the analysis:\n\nLet's assume that it's an n digit number with digits x_1, x_2, ...  x_n. Then\n  N = Sum{i=1..n}(10^(n-i)*x_i)\nand the number you get by moving the last digit to the front will be:\n  10^(n-1)*x_n + Sum{i=1..n-1}(10^(n-i-1)*x_i)\nWhat you are asking for is:\n  1.5*Sum{i=1..n}(10^(n-i)*x_i) \n    = 10^(n-1)*x_n + Sum{i=1..n-1}(10^(n-i-1)*x_i)\nor:\n  1.5*x_n + 1.5*Sum{i=1..n-1}(10^(n-i)*x_i) \n    = 10^(n-1)*x_n + Sum{i=1..n-1}(10^(n-i-1)*x_i)\nor by transposing to the other side:\n  1.5*Sum{i=1..n-1}(10^(n-i)*x_i) - Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 10^(n-1)*x_n - 1.5*x_n\nor: \n  Sum{i=1..n-1}(1.5*10^(n-i)*x_i) - Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = (10^(n-1)-1.5)*x_n\nor:\n  Sum{i=1..n-1}(15*10^(n-i-1)*x_i) - Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = (10^(n-1)-1.5)*x_n\nor:\n  Sum{i=1..n-1}(14*10^(n-i-1)*x_i)\n    = (10^(n-1)-1.5)*x_n\nor:\n  14 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = (10^(n-1)-1.5)*x_n\n\nNow the left hand side is a positive integer and on the right hand side 10^(n-1)-1.5 will be a fraction ending in 0.5. So x_n has to be an even digit to make (10^(n-1)-1.5)*x_n a positive integer. \n\nNow, if x_n were 2 or 6, multiplying it with something-point-five will give you an odd number. But the left hand side is an even number (because you are multiplying by 14). So x_n cannot be 2 or 6. That leaves 4 and 8 as the two possible choices for x_n i.e., the number N has to end in either 4 or 8.\n\nIf x_n is 4, then we are looking for:\n  14 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = (10^(n-1)-1.5)*4\nor:\n  14 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 4*10^(n-1)-6\nor: \n  7 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 2*10^(n-1)-3\nor:\n  7 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 2*10^(n-1)-3+10-10\nor:\n  7 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 2*10^(n-1)-10+7\nor:\n  7 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 20*10^(n-2)-10 + 7\nor:\n  7 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 10*(2*10^(n-2)-1) + 7\nor:\n  Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = 10/7*(2*10^(n-2)-1) + 1\n\nAgain, the left hand side is a positive integer. The right hand side can be a positive integer only if 2*10^(n-2)-1 is a multiple of 7. \n\nFor values of n, 2*10^(n-2)-1 is 1(n=2), 19(n=3), 199(n=4), 1999(n=5), 19999(n=6), etc. n=6 is the first number in this series (19999) that's a multiple of 7. Putting n=6, we get:\n  Sum{i=1..5}(10^(5-i)*x_i)\n    = 10/7*(2*10^(6-2)-1) + 1 = 28571\ni.e., a five digit number = 28571.\n\nThat gives us our first answer: N = 285714 and 1.5N = 428571.\n\nNow I have only done the analysis so far for x_n being 4. If you do similar analysis for x_n=8, you get\n  14 * Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = (10^(n-1)-1.5)*x_n\n    = (10^(n-1)-1.5)*8\n    = 8*10^(n-1)-12\n    = 8*10^(n-1)+2-14\nor:\n  Sum{i=1..n-1}(10^(n-i-1)*x_i)\n    = (4*10^(n-1)+1)/7 - 1\n\ni.e., 4*10^(n-1)+1 has to be a multiple of 7. For various values of n, 4*10^(n-1)+1 gievs you numbers like 41, 401, 4001, 40001, etc. and the first number in this series that's a multiple of 7 is 400001 for n=6. So we end up with:\n\n  Sum{i=1..5}(10^(5-i)*x_i)\n    = (4*10^(6-1)+1)/7 - 1 = 57142.\n  \nThat gives us our second answer: N = 571428 and 1.5N = 857142.\n\nWhile this is also correct, the first number is smaller. So the smallest number that satisfies your constraint is 285714.
31140
well, you look at the biggest digit, not including the sign.  lets say it is -7-5.  7 would be the biggest.  Then, see if its subtract or add.  This is add.  It has to be negative, since its a -7.  Another example is 7-9.  9 is the biggest, and since its a negative, the answer is a negative. One last one.  -2+9.  9 is the biggest, and since its possitive, the answer is positive.