The Magic Café
Username:
Password:
[ Lost Password ]
  [ Forgot Username ]
The Magic Cafe Forum Index » » Puzzle me this... » » Divisible by 3, 5 and 7? (0 Likes) Printer Friendly Version

Scott Cram
View Profile
Inner circle
2677 Posts

Profile of Scott Cram
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, two-digit 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
View Profile
Loyal user
London
284 Posts

Profile of pxs
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
151-105 = 46

(Not sure why you have to multiply first number by 70 rather than 35, though. Hmmm....)
Scott Cram
View Profile
Inner circle
2677 Posts

Profile of Scott Cram
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
116-70=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
193-70=123
123-70=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
View Profile
New user
52 Posts

Profile of Chout
What's that? Could you provide a link? I tried a google search, but to no avail.
Scott Cram
View Profile
Inner circle
2677 Posts

Profile of Scott Cram
drkptrs1975
View Profile
Elite user
North Eastern PA
452 Posts

Profile of drkptrs1975
That is pretty good
The Magic Cafe Forum Index » » Puzzle me this... » » Divisible by 3, 5 and 7? (0 Likes)
[ Top of Page ]
All content & postings Copyright © 2001-2020 Steve Brooks. All Rights Reserved.
This page was created in 0.16 seconds requiring 5 database queries.
The views and comments expressed on The Magic Café
are not necessarily those of The Magic Café, Steve Brooks, or Steve Brooks Magic.
> Privacy Statement <

ROTFL Billions and billions served! ROTFL