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Sagot :
We hava a basket of eggs, but we don't know how many there are in the basket.
Lets call X the number of eggs in the basket.
We know that if we take 3 eggs at a time or 7 eggs at a time, there are one egg left in the basket.
That means the residual of the division X/3 and X/7 is 1.
We know that if we take 8 eggs at a time, there are no eggs left in the basket.
That means the residual of the division X/8 is 0 (or X is multiple of 8).
We also know X is less or equal to 100.
[tex]\begin{gathered} X-3m=1 \\ X-7n=1 \\ X-8h=0 \end{gathered}[/tex]We have to find a number that is divisible by 7 and 3, and then add 1 and verify that is divisible by 8.
As 7 and 3 have no common denominator, we have to find a number that is divisible by 7*3=21 and then add 1 and verify that is divisible by 8.
We can check one by one:
If we add 1 to 21, we have 22. It is not divisible by 8, so it is not the value of X.
The next number is (2*21) + 1 = 42 + 1 = 43. It is not divisible by 8.
The next number is (3*21) + 1 = 63 + 1 = 64. It is divisible by 8, so this is the value of X.
The number of eggs in the basket is 64.
Equations
X-21n=1
X-8m=0
8m=1-21n
m=(1-21n)/8 and m has to be a positive integer.
We can iterate n=1,2,3.... until we find an m that is a positive integer.
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