M i n d s p O r T The Wake Up Caller

E4 Say it’s four in the AM, when the phone blasts you out of a pet dream. Before you can pour scalding bed tea into the instrument, a mellifluous voice informs you that the square of your six- digit telephone number ( from the 1960s no doubt) is exactly one greater than twice the square of her six- digit number. Meanwhile you begin loudly tracing her lineage back to an embarrassing hushed up event in the third quarter of the 17th century.

“Isn’t that amazing?” she asks, cutting into your invective, smoother than a pat of South American butter. “It sure is,” you reply, panting with undeleted expletives. “Is that how you got my number?”

“Yup,” she answers. “Nowif you can get mine we could repeat that magnificent flaw in my family tree all over again.”

DEAR MS ( The problem was: “You have three closed doors. Behind one is a sports car; behind the other two are goats. The host asks you to pick a door, and you select door # 1. The host, who is aware of what’s going on opens door # 3, revealing one of the goats. Should you now stick to door # 1, or switch to door # 2?”— MS)

Goat- FOR- BROKE Dept: This is known as the “Monty Hall Problem” as Monty Hall was the host of the game show Let’s Make A Deal. Every door has a 1/ 3 chance of having the car. So door # 1 has a 1/ 3 chance of having the car and doors # 2 and # 3 have a 2/ 3 chance. If door # 3 is revealed to have a goat, or a ‘ zonk’ ( as on the show), the 2/ 3 chance is concentrated on door # 2. So switch. Of course, this will work only 2/ 3 of the time. If you want your house teeming with sports cars, go for it. If you do this with 100 doors and the host opens all but one and the one you picked, the odds are 1/ 100 to 99/ 100. You can almost feel it unlike in the insignificant 1/ 3 difference. Only 13 per cent of people switch. So actually, the more doors the better!

( The other problem was about completing a 3x3 square grid with one number already inserted in and some extra given conditions. — MS)

MAGIC- SQUARED Dept: If the number in the middle square is the average of the two numbers above and below it, there are only six prime numbers which add up to 1 and then divide by 2 to give a prime number: 3, 5, 13, 37, 61, 73. After some combinations you find out the number in the middle square of the first row is 73. Then you can find all the third row numbers. So the numbers in the first row are: 7, 73, 31; the numbers in the second row are: 61, 37, 13; the numbers in the third row are: 43, 1, 67. The sum of the numbers in rows, columns and diagonally is 111.

— Dhruv Narayan, dhruv510@ gmail. com

The only numbers which can fit inside the middle square ( to satisfy the average of two numbers condition) are 19, 31 and 37. Then doing some shuffling we can get the required 3x3 grid ( totalling 111) as follows. Row 1: 31, 73, 7; Row 2: 13, 37, 61; Row 3: 67, 1, 43.

— Saifuddin Khomosi, saif_ sfk@ hotmail. com

Follow the procedure given: ( 1) List prime numbers < 100; ( 2) Filter out the prime numbers p from the set such that ( p + 1)/ 2 is also prime. This set consists of 13, 37, 61, 73; ( 3) From the above set, filter out the numbers such that p + 1 can be expressed as the sum of three different prime pairs. Only 73 satisfied this ( 73 = 67 + 7, 61 + 13, 43 + 31). ( 4) Fitting the numbers in the positions to also satisfy the requirement that the third largest number ( 13) is not in the rightmost column.

— K Sathyadev, sathya2008k@ gmail. com

ENDGAME Consider the following list of words: SCHWA, SPLAT, THREE, GRIST, CHORE, FLOUR, SCEAU, FILCH, RINSE, GAMES, CANOE, REACH, MOIRÉ, BEAUX, QUEUE, ANGST, INTRO, ASTER, ACHOO, EXIST, AWAKE, ABOUT, ADIEU, EIGHT, OUTDO, OILED. What’s the logic behind this particular word sequence?

( Mukul can be reached at mukul. mindsport@ gmail. com)