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Missing numbers on two spun discs
By Anonymous on Saturday, January 13, 2001 - 12:53 pm:

Numbers are marked on the 2 faces of 2 discs. One has the number 7 on one face, the other has four on one face. You do not know what is on the other face of each disc.
When the discs are spun the possible totals are the consecutive numbers 8,9,10,11.
The numbers on the reverse of each disc are 5 and 3 or 6 and 2. I found these using trial and error. Is there another method eg algebra?

I have used other consecutive totals and gained accurate results again through trial and error.
Is there a pattern or rule for the results??

Investigate the numbers on discs??

By Dave Sheridan (Dms22) on Tuesday, January 16, 2001 - 01:04 pm:

This problem is reasonably simple and translates to a set of simultaneous equations.

We know that 11 comes from 4+7. Lets call the other numbers x (on the 7 disc) and y (on the 4 disc). We know that x<7 since otherwise x+4 would be greater than 11. Similarly, we know that y<4 because y+7 is less than 11. This means that the smallest sum must be x+y. So our equations must be either

x+y=8
x+4=9
y+7=10

or

x+y=8
y+4=9
x+7=10

Which gives the two answers you've found.

That's about as algebraic as I can come up with. You can use the equations, replacing the numbers 8, 9 and 10 with others, to investigate what happens in different situations. Is it always possible to solve this problem, or can you find some numbers for which there is no solution?

-Dave