0 0 0 0 = = 0 × 0 0 × 0
Is it possible to put one of the integers 1 , 2 , … , 8 into each of the boxes, such that all of these numbers are used and both equations are true?
Clarification : Both the equations above represents a 2-digit integer that can be expressed as the product of two single digit integers.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Yes. Observing that the first digit of the 2-digit integer must be 5 is the most important step. Thank you for your solution
Conveniently, (and uniquely), 1 2 = 3 × 4 and 5 6 = 7 × 8 .
@Brian Charlesworth ahhhhh......interesting! Thank you! (+1)
Hence, the title of the problem.
56=7x8 12=4x3 Used all integers from 1 to 8
Problem Loading...
Note Loading...
Set Loading...
Relevant wiki: Modular Arithmetic - Problem Solving - Basic
For interest, one way to arrive at the solution quickly is to notice that the number 5 can only be placed in the leftmost slot. Anywhere else will imply multiplying by 5, which will need another 5 or a 0, which is not allowed. Thus the 2 digit number is between 51 & 58. Only 5 6 = 7 × 8 works. 1 - 4 are remaining and only 3 × 4 gives a 2 digit number (12). 5 6 = 7 X 8 1 2 = 3 X 4