1. The following words can be divided into five sets of size 1, 2, 3, 4 and 5. Each set is associated with a word of that length, and these words grow incrementally (eg A-AN-PAN-PAIN-PAINT). What are the sets?
DEMURE EDGE EYE FORMAL INSTANT
MERIDIAN MESSAGE MINISTER NUMBER
OUTER PROPER RIB STUFFY TIME WHEEL
2. Find m such that 700! × 699! × 698! × … × 1! × m! is a perfect square.
Advertisement
3. Which is the odd word out?
ALLSPICE, EMMANUEL, GERIATRIC, MELBOURNE, MELCHIOR, VICTORIANA
Scroll down for answers
Answers
1. {EYE} – homophone of I; {INSTANT, MESSAGE} – IM initialisation; {WHEEL, OUTER, EDGE} – definition of RIM; {DEMURE, FORMAL, PROPER, STUFFY} – synonyms of PRIM; {MERIDIAN, MINISTER, NUMBER, RIB, TIME} – can follow PRIME.
2. m= 350. Note that 700! × … × 1! = 700 × (699!)^2 × 698 × (697!)^2 × … 2 × (1!)^2, so this is (700 × 698 × … × 2) = 2^350 × (350!) times a perfect square.
3. ALLSPICE. The others begin with the name of a Spice Girl: EMMAnuel,
GERIatric, MELBourne, MELChior, VICTORIAna – ALL the SPICE girls, in fact.