The Berry Mystery
In the kitchen, there was a bowl of berries.
When Billy walked by, he took 1/2 of the berries and 2 extra.
Later Bob walked by, and he took 1/3 of what Billy took and 2 extra berries.
Soon Joe walked by, and took 1/3 of what Bob took and then put 1 of those berries back into the bowl.
Sometime afterward, their mom walked by and saw only 1 berry remaining in the bowl.
How many berries were originally in the bowl?
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1 solution
If there are x berries in the bowl, then Billy took 2 x + 2 .
Bob took one third of what Billy took plus 2, which means 2 x + 2 is multiple of 3.
2 x + 2 = 3 m , 6 m − 4 = x , x ≡ 2 ( m o d 6 ) , hence 20 is the only option which will fit.