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Is it possible to make 10000 out of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only the sum operator and using all the digits exactly once?No, at least not without doing something cute and tricksy, like turning a digit sideways or whatever.The remainder of any number with respect to 9 is the modulo 9 sum of the digits of that number. So for instance, the remainder of 12345 with respect to 9 is (1+2+3+4+5) mod 9 = 15 mod 9 = 6. (12345 = 1371*9 + 6). The remainder of the sum of two numbers with respect to 9 will be the modulo 9 sum of their individual remainders. So the remainder of any number formed using the digits 0...9 and the sum operator with respect to 9 will be the modulo 9 sum of the digits 0...9. Which is 0. So, however you arrange the digits, the sum will be divisible by 9.10,000 is not divisible by 9, so it cannot be formed using such an arrangement of digits.(If "cute" solutions are permitted, then all bets are off; for instance, I can turn the digit '1' sideways to form a minus sign, and get 4032+5976-8=10,000.)
How many 5 digit numbers are divisible by 4 out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9?All numbers ending with 00,04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 are divisible by 4 because if last two digits is divisible by 4, then entire number is divisible by 4.Using CombinatoricsTen thousand'th digit can be 9 waysThousand'th digit can be 10 waysHundred'th digit can be 10 waysIf Tenth digit is 0, then unit place 3 ways.=> 9 x 10 x 10 x 1 x 2 numbersIf Tenth digit is 1, then unit place 2 ways.=> 9 x 10 x 10 x 1 x 2 numbersIf Tenth digit is 2, then unit place 3 ways.=> 9 x 10 x 10 x 1 x 3 numbersIf Tenth digit is 3, then unit place 2 ways.=> 9 x 10 x 10 x 1 x 2 numbersIf Tenth digit is 4, then unit place 3 ways.=> 9 x 10 x 10 x 1 x 3 numbersIf Tenth digit is 5, then unit place 2 ways.= 9 x 10 x 10 x 1 x 2 numbersIf Tenth digit is 6, then unit place 3 ways.=> 9 x 10 x 10 x 1 x 3 numbersIf Tenth digit is 7, then unit place 2 ways.=> 9 x 10 x 10 x 1 x 2 numbersIf Tenth digit is 8, then unit place 3 ways.=> 9 x 10 x 10 x 1 x 3 numbersIf Tenth digit is 9, then unit place 2 ways.=> 9 x 10 x 10 x 1 x 2 numbersTotal Numbers = sum of all above= 9 x 10 x 10 x 25= 22500Alternate Easy MethodFirst number = 10000Last number = 99996Number of numbers divisible by 4 is :(99996 - 10000)/4 + 1 = 22500:-)
If 4/7 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?4/7=2min.1/7=2:4min.=0.5min.7/7=0.5*7 so7/7 will fill in 3.5 min.
How do I amplify a voltage of 2.4-2.7 volts to 0-5 volts?To amplify a voltage of 2.4-2.7 volts to 0-5 volts, it is required to configure op-amp as shown below so as to output in the form of [math]Output=m*Input-C where m=16.6667 & C=40. [/math]If reference voltage of 5V is available then circuit with following values amplify a voltage of 2.4-2.7 volts to 0-5 volts
How do I amplify a voltage of 0.7 volts to 2.7 volts?A voltage amplifier in simplest form is any circuit that puts out a higher voltage than the input voltage.
How can I learn to remember multiple single digits, that are read out loud to me? I will only hear the number once like: “0-4-7-9-2-3-5-6-8-1-2-0-6-2”. I will not have time to study the numbers. They are read out loud to me once. How?I read this book about Super Power Memory written by Harry LorraineHe used Pegging - link systemFirst you need to memorise thisThe numbers from 0 - 9 are link to sounds of the lettersThere are about 26 chapters in this book and if want to remember long numbers, dates, faces , playing cards and so on ,the writter clearly says that it's important not to skip any lesson if you want to master the systemPlease read this bookYou will probably need a lot of practice too after having read the book
How hard is to have a GPA of 7.0 (out of 10.0) in universities in the Netherlands?My professor would say10 is for God9 for the professorand 7 for an excellent student.At the university 10's are rarely given as there is always room for improvement. That makes 9 the highest possible. 8 is more in signNow but you definitely need to work hard.On the contrary the passing grade 6, is rather easily obtained if you have a decent set of brains and attend the lectures. But there is a funny twitch here. At the university you often are graded for your attitude as well. So, if you attend all lectures, have a good set of brains and have a can-do attitude you should get a 7 average.