

Scott Cram Inner circle 2677 Posts 
The math teacher asks one of his students to think of any whole number from 10 to 99. (Just for example, we'll say the number is 46.)
The teacher then asks, "When you divide your number by 3, what is the remainder?" The student, in our example, says, "1." Next, the teacher asks, "When you divide your number by 5, what is the remainder?" Continuing with our example, the student says, "1." One last time, the teacher asks, "When you divide your number by 7, what is the remainder?" Finishing up our example, the student says, "4." The math teacher almost immediately says, "Your number was 46." No matter which whole, twodigit numbers are chosen, the teacher asks these same three questions, and is immediately able to give the number that was chosen. Since there are no stooges involved, and the only information he has to work with is the remainders after dividing by 3, 5 and 7, what is the process used by the teacher determining the number? 
pxs Loyal user London 284 Posts 
Multiply the first number by 70 (multiple of 5x7), the second by 21 (3x7), and the third by 15 (3x5). Add these together. Then subtract as many 105's (3x5x7) as possible.
So (70x1) + (21x1) + (15x4) = 151 151105 = 46 (Not sure why you have to multiply first number by 70 rather than 35, though. Hmmm....) 
Scott Cram Inner circle 2677 Posts 
Not bad!
In the traditional method, 70 is used because it's easier to multiply by. You just multiply by 7, and add a 0. If you prefer to use 35 instead of 70, multiply the first number by 35, proceed as above, and subtract as many 70's as you can, instead. (35x1) + (21x1) + (15x4)=116 11670=46 Here's another number, this time with remainders of 2 (when divided by 3), 3 (when divided by 5) and 4 (when divided by 7): (35x2) + (21x3) + (15x4)=193 19370=123 12370=53 For an even more intriguing method, check out Ibidem 14, in which they print a method that requires absolutely no calculation, yet still yields the correct answer! 
Chout New user 52 Posts 
What's that? Could you provide a link? I tried a google search, but to no avail.

Scott Cram Inner circle 2677 Posts 

drkptrs1975 Elite user North Eastern PA 452 Posts 
That is pretty good

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