Four-year-old Gina has a brand new set of bright green alphabet blocks. Each of the four blocks has a single letter on each of its six sides. (Yes, yes we all know six fours are twenty-four so that two letters must be missing. Therefore to help your doubting and deeply agonised soul V and Z are not there. Happy?) By arranging the blocks in various ways this genius kid can apparently spell all of the following words: CHIP, FLUX, FUNK, IRAQ, JOBS, JUMP, QUIT, SKEW, SMOG, SWAB, TUCK and WILD.
How on Earth a four-year-old can possibly know how to spell Iraq without putting a C or a K in it somewhere considering I didn’t even know how to spell a bird in a bush till some non-existent weapons of mass destruction landed on my lap by mistake is still a puzzle.
Anyway to cut the faff from the fluff finally, you have to now figure out how the letters are arranged on Gina’s four blocks.
(The two remaining questions in the BGTN section were: “(3) If we replace the 4 and 7 by arbitrary numbers A and B, under what condition can the number of birds be infinite? (4) If the number of birds is not infinite, what is the maximum number of birds on the wire for a given A and B?”)
Let M = abs(A - B), N = minimum(A, B) + 1. Then if the absolute difference of any two members of the set S = (0, M, N, 2M, M + N) is 1, then the sequence is finite; otherwise, it is infinite. (4) Let D be the minimum number in S such that its absolute difference with any other member is 1. Then, maximum length is 1 + D + N. -- Dhruv Narayan, firstname.lastname@example.org
(The second problem was: “Find a 10-digit number whose first digit is the number of 1s in the number, second digit the number of 2s in the number, etc. Answers can’t start with a zero.”)
Starting with the 10th digit, its value should be zero as any value greater than zero will result in a 11 digit number. Now if the 9th digit is 9 we will get 9999999990,which will violate conditions for 1st, 2nd, etc. 9th digit also can’t be 1 as the presence of digit 9 on any of 1-8th place will result in 9 times repetition of that place which is impossible as we have only 7 places left to fill. So the 9th place is also zero. Similarly going backwards to fill the digits we get 1000000000. -- Abhishek Narayan, email@example.com (Yes Rekha G, firstname.lastname@example.org you got that answer too. However, these are not the most elegant of solutions.)
If the rankings given to the digits in the 10-digit number are 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 then the answer is 2100010006. Alternately, if the rankings given to the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 then the answer would be 6210001000. -- Narayana Murty Karri, email@example.com
The Pigeonhole Principle is used in finding out the 10-digit number. In this principle, exactly one of the (9 - n) numbers is equal to 2 and all other nonzero numbers are equal to 1 which means (8 - n) numbers equal to 1. Using this method the 10-digit number is 6210001000. -- Shashi Shekher Thakur, firstname.lastname@example.org
Solution was quite easy but checking on the uniqueness took time. The solution is 1000001007. This is unique because for a 10-digit number, the first digit should be a non-zero number and any other number other than 1 means you have to use 1 that many times in other places which in turn demands the number of the respective place’s digit (where 1 is put) to be repeated. -- Mridula Patnaik, Bhubaneswar (email ID withheld on request)
BUT GOOGLE THIS NOW
1. The equations below are written in a code such that each digit shown represents some other digit. Break the code, given that each of the following is true in base 10. 8 + 7 = 62; 5 + 3 = 5; 12 + 8 = 23; 50 + 9 = 54; 11*1 = 55; 0 - 9 = 1.
2. The way these following things work is like this: You get a conundrum for instance saying UNCERTAINTY is to HEISENBERG as UNDECIDABILITY is to ? and of course the easy answer is GODEL! Ta daaa. So try this for size: FIRST is to SECOND as TYPEWRITER is to?
Sharma is a scriptwriter and former editor of Science Today magazine.(email@example.com)