In the meantime, try this on for size: Can you convert the string 'AT' to 'AS' using the following four rules?
Published: Thu 26 Nov 2015, 11:00 PM
Last updated: Fri 27 Nov 2015, 9:50 AM
E4
Okay guys (and I'm obviously also addressing the not-guys out there, who are just as important), there's something that needs to be sorted out. It's like this: some countries use hundreds, thousands, millions, billions, trillions and so on - and some countries often don't. For instance, in the subcontinent, where they also use lakhs and crores and sankhs and stuff. No system is the right one per se, but when you submit answers to problems that involves largish numbers, it would really help yours truly sitting out here if you didn't nicely mix up the two with comma separators floating around like UFOs in Close Encounters of the Numerical Kind. Get the drift? We're talking major mothership blues here. For the record though, we try to follow the international notation for uniformity. See if you can manage too.
In the meantime, try this on for size: Can you convert the string 'AT' to 'AS' using the following four rules? (1) You can add 'T' at the end of a string ending with 'S'; (2) For a string 'Ax', you can write it as 'Axx'; (3) Whenever you find a 'TTT' string, you can turn it to an 'S'; (4) Whenever you find an 'SS', you can remove it from the string.
DEAR MS
(The problem was to fill in the actual number of 0s, 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s and 9s occurring in a given box - including the filled in answers. - MS)
1's-Is-Not-Enough Dept:
The blanks must be filled as 1, 7, 3, 2, 1, 1, 1, 2, 1, 1. The number of 0's will obviously be one, as all digits occur at least once. Most other digits will be one, except the digit representing the number of 1s, which will occur twice, hence increasing the number of 2s. The 2s can't be two, as then there will be three 2s in total. Thus, there should be three 2s and two 3s, leaving the six digits to be 1, making the number of 7s, two.
Answer can be found just through trial and error before you realise all of them should be single digit answers and there are two times that 7 appears on the sheet. Then you see all of them fall in place.
Saifuddin's box is nowhere close to Pandora's. The solution is a no-brainer. Here goes: Fill in the blanks with this sequence: 1, 11, 2, 1, 1, 1, 1, 1, 1, 1.
(The other problem was: "If you were to write down the numbers from 1 to 1,000,000 in order, how many digits would you use? Also, how many zeros would you use?" - MS)
Digital-Divide Dept:
I would use a total of 5,888,896 digits. Moreover, the number of zeros needed to write from 1 to 1,000,000 is (starting from units place, then tens place and so on): 99999 + (99999 - 9) + (99999 - 99) + (99999 - 999) + (99999 - 9999) + 6 = 488895.
(The last problem was: "How will an astronaut use a pan balance to weigh 5kg while in a rocket travelling in space with no gravity? Will the scales tilt towards the heavier end?" - MS)
How-It-Pans-Out Dept:
Simple: without gravity (or acceleration), weight cannot be measured. Only mass can be. Therefore, the pan will not dip.
ENDGAME(S)
- Why is the temperature on the planet Venus generally hotter than the planet Mercury, even though Mercury is much closer to the Sun?
- You have a mini chessboard with four rows and five columns. The squares are numbered from 1 to 20, with the first row containing numbers 1-5, second row 6-10, third row 11-15 and the last row 16-20. You have to start from number 1 and reach number 20, while touching all the squares exactly once and reach square 20, making a knight's move, as in chess.
(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)
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