An experimental method for defining the kilogram in terms of properties of nature is now more accurate than ever, according to the scientists at the US National Institute of Standards and Technology (NIST). This may take the scientific community closer to redefining the kilogram, one of the seven basic units of the international measurement system still defined by a physical artifact. The latest NIST work confirms the instituteís 1998 results, but reduces the measurement uncertainty by about 40 per cent. Scientists at NIST and other institutions around the world have spent years conducting experiments to arrive at a reliable definition of a kilogram, replacing the current international standard for it, a century-old cylinder of platinum-iridium alloy about the size of a plum. The new experiment done by the NIST experts used an apparatus called the watt balance or electronic kilogram. The man on the street wonít be affected by the expertsí urge to redefine a kilogram. But the endeavour reveals one thing: scientistsí longing for accuracy.
PUZZLE 1 35 containers of total weight 18 units must be taken to a space station. One flight can take any collection of containers weighing 3 units or less. It is possible to take any subset of 34 containers in 7 flights. Is it possible to take all 35 containers in 7 flights'
PUZZLE 2 Write down a row of arbitrary integers (repetitions allowed). Then construct a second row as follows. Suppose the integer is in column k in the first row. In column k in the second row write down the number of occurrences of in row 1 in columns 1 to k inclusive. Similarly, construct a third row under the second row (using the values in the second row), and a fourth row. An example follows:
7 1 2 1 7 1 1
1 1 1 2 2 3 4
1 2 3 1 2 1 1
1 1 1 2 2 3 4
Is the fourth row always the same as the second row'
Solutions on October 3
Soumava Chakraborty; Prasenjit Das, Ranchi; Bappa Sutradhar; Debasis Ganguly, Alumnus Software, Cal-91; S.P.S. Jain, New Delhi; Arun Kumar Samadder, Cal-25; P.K. Iyengar, Bokaro Steel City; C.K. Duttagupta; Arundhati Subramanian, Jamshedpur
Santosh Kumar Gupta, Rourkela; Sandeep Ghosh, Howrah; Debjani Garai, Behala; Bappaditya Sen, Teghoria; Subha Saha, St Xavierís Instn, Sodepur; Jyotirmoy Dey, Jadavpur; Prasanta Dutta, Bankura; Sushil Roy
Please send in your entries to email@example.com within 10 days. Send us complete solutions, not one-line answers.
Solution 1: We can write the condition as b-a=d-c, so the 10 numbers in the first row and 1 in the second row can all be chosen arbitrarily. Hence at least 11 questions are needed. But they are also sufficient. Having determined those numbers, the others immediately follow.
Solution 2: (a) True, (b) False and (c) False
I didnít have enough space to explain solution 3 for the puzzles set on August 29. Let me explain it here. At most four competitors can receive a rank 1. For a competitor with a rank 1 can only receive ranks 1, 2, 3 or 4. There are only 36 such ranks available and each competitor with a rank 1 needs 9 of them. If only one competitor receives a rank 1, then his score is 9. If only 2 competitors receive rank 1, then one of them must receive at least five rank 1s. His maximum score is then 5.1+4.4=21. And so the argument goes.