A total of 37 candies are placed in 7 jars. Each jar has different number of candies. No jar has exactly 5 nor 6 candies. No jar is empty. What is the greatest number of candies that any one jar can have?
2026-03-28 08:09:51.1774685391
What is the greatest number of candies that any one jar can have?
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Let us fill 6 jars with the least possible amount then just place the rest in the remaining jar.
You put 1 candy in the first jar, then 2 candies in the second jar, 3 in the third jar, 4 in the fourth jar. You cannot put 5 or 6 candies, so you have to put 7 candies in the fifth jar and 8 candies in the sixth jar.
That is a total of $1+2+3+4+7+8=25$ candies in the jars. You start off with 37 and you spent 25, that means there is $37-25=12$ candies left for the seventh jar, which is the largest amount possible.