Solution Step 0/0
The school board was arranging some holiday gifts for elementary school graduating students for the upcoming New Year's Eve celebrations.
After distributing candies and cookies in the gift packages, the school board began with the oranges. But it was calculated that if 10 oranges are put to a package, one package would only get 9; if 9 oranges are put to a package, one package would only get 8; if 8, 7; if 7, 6; and so on down to 2 oranges per package with one package getting only 1 orange.
What is the least amount of oranges the school board had at its disposal?
After distributing candies and cookies in the gift packages, the school board began with the oranges. But it was calculated that if 10 oranges are put to a package, one package would only get 9; if 9 oranges are put to a package, one package would only get 8; if 8, 7; if 7, 6; and so on down to 2 oranges per package with one package getting only 1 orange.
What is the least amount of oranges the school board had at its disposal?
Explanations
With 1 one orange their number would have been divisible by 10, 9, 8, ..., 1. The lowest common multiple (LCM) for numbers 1 through 10 is 2,520.Thus, the school board had 2,520 - 1 = 2,519 oranges, or if more, then it would be: 2,519 + 2,520n, where n is any positive number.
[After Boris A. Kordemsky. The Moscow Puzzles: 359 mathematical recreations. 1972]
Check between 500 & 1,000
Check between 1,000 & 1,500
Check between 1,500 & 2,500
Check between 2,500 & 3,000
