[quote name='PenguinMaster']Extremely easy problems, try to find something challenging.[/quote]
1. There are two mathematicians, Bill and Dan on a train talking. Dan says to Bill "I know you have 3 children. How old are they?" Bill says "The product of ages of my children is 36, and the sum of their ages add up to my old football jersey number." Dan says "That doesn't tell me anything." Bill says "Oh. My youngest son has red hair." Dan says "Oh, NOW I know how old they are."
How did Dan know how old the children are, and what are their ages?
2. It’s 10:00 on a Saturday morning, and five of the residents of Oceanside Manor are in the laundry room doing their wash. Except for one of the washing machines, which is out of order, all of the machines, which face outward from the utility island, are in use. Each washer is programmed for one of three temperatures (cold, hot, or warm) and one of three settings (delicate, normal, or permanent press). Presently, each of the nine washers in use has a different number of whole minutes left in its cycle. From the information provided, can you determine the name of the resident using each washing machine (lettered A through J in the illustration), each machine’s temperature and setting, and the number of minutes left in its cycle, as well as which one is out of order. Note: Each washer is adjacent to two others. Washer E is back-to-back with washer J. The prime numbers from 2 to 35 are 2, 3, 5, 7, 11, 13, 17, 19, 29, and 31.
1. No two machines operating at the same water temperature are also operating on the same setting.
2. Each washer has at least two minutes left in its cycle.
3. Only one resident is using more than two machines.
4. One resident is using both the washer that is back-to-back with the out-of-order machine and one that is adjacent to the out-of-order washer.
5. No two adjacent machines have either the same water temperature or the same setting; the two machines adjacent to the out-of-order one also have different temperatures and settings.
6. The five pairs of back-to-back washers are, in some order, the pair that includes the out-of-order machine, a pair being used by Bob and Ford, another pair being used by Bob and Ford, the pair that includes the only washer being used by Sally, and the pair that includes the only washer being used by Margie.
7. The sum of the times remaining on all machines being used by any one resident does not exceed 35 minutes; the sum of the times remaining on any pair of back-to-back machines does not exceed 35 minutes.
8. Exactly four of the numbers of minutes remaining are prime numbers; one of the washers has a time remaining that is a multiple of three of these numbers.
9. Three times as many minutes are remaining on Margie’s washer than are remaining on one of Ford’s washers.
10. Ford has one more minute remaining on one of his machines than he does on another of his machines.
11. Sally has one more minute remaining on her washer than Bob does on one of his; the number of minutes left on Sally’s machine is a multiple of the number of minutes left on the washer back-to-back with hers.
12. The washer with the highest number of minutes left is being used by Janet.
13. Six washers, in consecutive clockwise order, are one being used by Ford, one Bob is using, the one using warm water on the permanent-press setting, the one that is back-to-back with the out-of-order machine, a washer operating on the permanent-press setting (which is back-to-back with the one using hot water on a delicate setting), and the washer with exactly 25 minutes remaining.
14. All of Bob’s washers are operating with the same setting, and all of Ford’s washers are operating at the same water temperature.
15. Janet isn’t using machine A, and Margie isn’t operating machine I.
16. Only three of the washers have less than ten minutes left on their cycles.
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