This is a collection of interesting problems aimed to improve your problem solving skills and simultaneously stimulate your interest in Mathematics.

Question 1: Some simple problems.

a) Simplify (x – a)(x – b)(x – c) . . . (x – z)

b) If you had only one match and entered a dark room in which there were a kerosene lamp and a candle. Which one should you light first?

c) You have fifteen cents in two coins. One of them is not a five cent coin. What are the coins?

d) There is three errers in this sentence. Can you find them all?

e) In a year how many months have 31 days, how many months have 30 days and how many months have 28 days?

f) You have three cups of coffee and fourteen lumps of sugar. You have to sweeten the cups using an odd number of lumps in each cup. How can you do it? (You must use all the lumps)

g) Can I find a trick recalling pi easily?

Answer

a) 0, as (x – x) is a factor, which is equal to 0. Anything multiplied by 0 is 0.

b) The match.

c) The other coin is 5c, and this one is 10c.

d) Is, Errers, and the fact that there are only two errors makes this another error.

e) Six months have 31 days, eleven months have 30 days and all twelve months have 28 days.

f) Put a lump in the first cup, a lump in the second cup and all twelve lumps in the third cup. This is a very odd number (to put 12 lumps in a cup of coffee).

g) Count the words (Count the number of letters in the question and answer sentences: 3 1 4 1 5 9 2 6 5 3 5)

Question 2: Time measurements.

a) You have two hourglasses, a four minute glass and a seven minute glass. You want to measure nine minutes using the two glasses. How do you do it?

b) You have two incenses which last one hour each. How do you use them to measure 45 minutes?

Answer 

a) Start both hourglasses. When the four minute glass runs out (4 minutes elapsed), turn it over. When the seven minute glass runs out (7 minutes elapsed) turn it over. When the four minute glass runs out the second time (8 minutes elapsed), turn the seven minute glass over (it has run for only 1 minute). When it stops, nine minutes have elapsed.

b) Burn both ends of an incense and only one end of the other incense. When the first incense burns out, (30 minutes elapsed), burn the other end of the second incense. When it burns out, it's 45 minutes.

Question 3: Sequences from the Alphabet.

a) What are the next three terms for the following sequences?

i) 8, 5, 4, 9, 1, 7, 6, . . .

ii) o, t, t, f, f, s, s, . . .

iii) 4, 8, 12, 2, 1, 7, 6, . . .

b) The letters of the alphabet can be grouped into five distinct classes. The first thirteen letters are shown. Place the remaining thirteen letters in their proper classes.

AM

BCD

HI

NS

FGJL

Answer 

a)

i) 3, 2, 0 (the first ten numbers (from 0 to 9) in alphabetical order: eight, five, four, nine, etc.)

ii) e, n, t (the initials of the first ten counting numbers: one, two, three, etc.)

iii) 3, 5, 11 (the months of the year in alphabetical order)

b) The five classes are: symmetrical about the vertical axis, symmetrical about the horizontal axis, symmetrical about both axes, having a point of symmetry and asymmetrical.

Thus,

TUVWY

EK

OX

Z

PQR

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