DEPARTMENT OF MATHEMATICS RAMANUJAN MORGANS MATH CLUB

 Decode the statements i) NHHS BRXU IULHQGV FORVH DQG BRXU HQHPLHV FORVHU ii) H V A I E A A E N C D Y

i) KEEP YOUR FRIENDS CLOSE AND YOUR ENEMIES CLOSER Giving Numerical values to the alphabets starting from zero and skipping three letters we get the sentence. ii) HAVE A NICE DAY

 (One quote is behind those numbers, find it)

 EVERY SQUARE MATRIX SATISFIES ITS OWN CHARACTERISTIC EQUATION.

Can you work out what Charlie's number is from these clues? C1: Charlie's number is palindromic, the second and third numbers are different. C2: Charlie's number is greater than 100 and is prime. C3: Charlie's number is odd. The difference between the largest and smallest digits is 5. C4: Charlie's number is less than The sum of the digits is 14. C5: Charlie's number is not divisible by 3. It is less than 500. C6: Charlie's number is a whole number with only two divisors.

 We know from clues C2 and C5 that Charlie's number is somewhere between It is palindromic, so the first number and the last number must be the same, but the middle number is different. Because it is an odd number, the last digit cannot be 2 or 4. This leaves 1 or 3. If the first and last digits were both 1, then the middle digit would have to be 12 for them to add up to 14, which isn't allowed. Therefore the first and last digit must be 3 and the middle digit must be 8. Just to check,383 is a prime number and the difference between 3 and 8 is 5, so this is definitely the right answer.

Finals Can you arrange 5 different digits (from 0 to 9) in the cross so that i) the total of the 4 outside numbers is equal to the middle number ii) the top 2 numbers multiplied together are also equal to the middle number iii) the sum of the 3 numbers forming a diagonal is equal to the other 3 numbers forming the other diagonal.

Raji had a pack of twenty cards numbered from 1 to 20. She arranged the cards into six unequal piles. The numbers on the cards in each pile added to the same total. What was the total and how could this be done?

i) 20,15 1,2,3,4,5,9,11 18,17 10,13,12 19,16 6,7,8,14 ii)20,15 1,14,11,9 10,19,6 3,4,12,16 17,13,5 2,7,8,18

Qn :006

 THE FIRST CIA HEADQUARTERS BUILDING IN 1947 WAS LOCATED AT 2430 E STREET, NW IN WASHINGTON