Problematics | To eat ice cream or not to...

Is a mathematical puzzle easier to solve than a word puzzle that requires you to derive a word or phrase from clues about the letters? I would have thought it was the other way around, which is why last week’s supposedly more difficult mathematical puzzle came before the supposedly easier word puzzle, but it appears that some readers found the latter more difficult.

Not that it matters, as long as readers find the puzzles fun to solve. This week’s puzzles, I think, are both on the easier side, although as usual it is readers who will be the best judges of that. The first is a logic puzzle and the second one involves number, but neither is traditionally mathematical.

#Puzzle 94.1

Three people hailing from three different states are colleagues in an office in Delhi. They lunch together at the canteen every afternoon but don’t necessarily eat the same items. They order different main courses, which is not relevant to this puzzle, after which each one may or may not order ice cream, which is relevant.

1. The woman from Andhra Pradesh orders ice cream only if one or both of her colleagues (one from Arunachal Pradesh, the other from Assam) order ice cream.

2. The women from Andhra Pradesh and Arunachal Pradesh never order ice cream together.

3. The woman from Andhra Pradesh must have ice cream unless neither of her colleagues orders ice cream for themselves.

4. If the woman from Assam does not order ice cream, either one or both of her colleagues must order it.

Who order(s) ice cream?

#Puzzle 94.2

Whenever we fill up dates in any form, we do so in a DDMMYYYY format these days. This makes sense because we are at that stage of the century when a person chosen at random may have been born in a year beginning either 19 or 20. In a digitised world, this format is likely to stay for all time to come, but it was not long ago when the standard format was DDMMYY, with YY representing the last two digits of the year. In our school notebooks, for example, we would enter March 23, 1978 as 230378. There would be slashes in between, but we can ignore them for the sake of this puzzle.

Which date(s) in independent India and British-ruled India, when written as DDMMYY on a piece of paper without slashes or dashes, read the same when the sheet is turned upside down?

MAILBOX: LAST WEEK’S ANSWERS

#Puzzle 93.1

Hi Kabir,

The boy is 24m from the tree's base when he picks up his kite from the ground. This is a classic Pythagorean problem, assuming of course that the tree is perfectly perpendicular to the ground. In this case, the vertical height of the right-angled triangle is 18m. If we use x as being the distance from the foot of the tree to the spot that the kite touched the ground, then the distance that the kite travelled (hypotenuse) is 54 – x (which is the distance that the boy ran). The Pythagorean equation is x² + 18² = (54 – x)². Solving this for x will give us x = 24m.

I am not sure if I enjoy the puzzles more or the historical knowledge about some great mathematicians or mathematical treatises that you present each week. It is immaterial though, as long as you keep them coming every week.

— Akshay Bakhai, Mumbai

#Puzzle 93.2

Solving for the two words that begin with same letter, we get some options. The ones that fit are accommodate = LODGE and grasp = LEARN, and collect becomes HOARD. We now get letters against the numbers (1 = G, 2= R, 3 = A, 4 = N, 5 = D, 6 = H, 7 = O, 8 = T, 9 = E, 10 = L). Actress’s name = GRETA GARBO; movie = GRAND HOTEL.

— Amarpreet, Delhi

Solved both puzzles: Akshay Bakhai (Mumbai), Amarpreet (Delhi), Shishir Gupta (Indore), Dr Sunita Gupta (Delhi), Professor Anshul Kumar (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Harshit Arora (IIT Delhi), Ajay Ashok (Mumbai), Sampath Kumar V (Coimbatore)

Solved #Puzzle 93.1: Yadvendra Somra (Sonipat), Raghunathan Ravindranathan (Coimbatore)

Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com