- There are ten boxes containing 4, 8, 27, 31, 34, 35, 44, 45, 51, and 59 balls of either red, or blue, or green in color.
- Some boxes contain only red balls, some boxes contain only blue balls, and remaining boxes contain only green balls.
- None of the boxes contain balls having more than one color.
One salesman sold
only one box out of them and he declared, "I have the same number of red, blue, and green balls left over."
Which box is sold out?
8.
Consider the numbers mod3. Their total is worth 2, so the number to be deducted must also be worth 2, mod3. Candidates are 8 (110), 35(101), 44(98), 59(93), where the figures in brackets denote 1/3 of the remaining totals.
If we take the first of these, 8, then 51+59=110 is an obvious candidate, and indeed (31+34+45) and (4+27+35+44) also add severally to the same figure.
Edited on April 29, 2022, 7:59 am
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Posted by broll
on 2022-04-29 07:52:22 |
Possible Solution
