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Mental Arithmetic (Posted on 2003-10-05) Difficulty: 3 of 5
I can multiply any three-digit number by 1667 in my head, usually in less than 10 seconds.

Also, to make it even more impressive, I come up with the digits of the result in proper order (not in reverse!)

How can I do this?

  Submitted by nellie    
Rating: 3.3333 (6 votes)
Solution: (Hide)
METHOD:

1667 is not used. The calculation uses your number only. It involves division not multiplication and hence the answer starts with the most significant digit.

Divide your number by 6. This gives the first 2 or 3 digits of the answer.

Multiply the remainder by 5.

Put this remainder by 5 in front of your original number and divide by 3. This gives the rest of the answer.

Example

1667 x 872

Divide 872 by 6 = 145 remainder 2

Mutiply remainder by 5 = 10

Put in front of number and divide by 3

10872/3 = 3624

Thus 1667 x 872 = 1453624

Look here for RoyCook's solution, look here for Gamer's solution, look here for mohan's solution.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Thoughts K Sengupta2023-05-17 23:09:02
a solution?mohan2003-10-16 01:17:00
re: gamer's replyGamer2003-10-15 19:51:52
gamer's replynellie2003-10-15 13:23:50
re: Mental ArithmeticGamer2003-10-14 17:23:54
Mental Arithmeticnellie2003-10-14 06:33:32
re: nonemohan2003-10-14 03:25:01
noneLee2003-10-13 12:26:47
Solutionsolutionmohan2003-10-13 04:45:20
Some ThoughtsNo Subjectmohan2003-10-13 04:42:39
re(2): solutionnellie2003-10-12 11:26:22
re: solutionmohan2003-10-06 01:42:22
a possible solution?mohan2003-10-06 01:32:25
Solutionre: another path?Gamer2003-10-05 14:57:13
re. another path?Lee2003-10-05 14:54:06
Some Thoughtsanother path?Charlie2003-10-05 14:36:43
alsoLee2003-10-05 14:23:41
solutionLee2003-10-05 14:09:50
SolutionsolutionRoyCook2003-10-05 12:58:01
Another ClarificationGamer2003-10-05 12:27:18
clarificationCharlie2003-10-05 11:22:39
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