Brain Teasers and Puzzles 

Workings

Hint
The 1^st word begins with the letter Z.

Answers
-e--a   = zebra   (ZBR) -ui-ar  = guitar  (GT) --ick   = quick   (QU) -a-     = sad     (SD) bo-     = box     (X) -owe-   = vowel   (VL) -on-ey  = monkey  (MK) -el     = eel     (E) ra-     = ray     (Y) ---kage = package (PAC) --ll    = will    (WI) mo--    = moon    (ON) -eap    = heap    (H) -eep    = jeep    (J) -un     = fun     (F)
Alternative Answers
Zebra, guitar, quick, jam, box, vowel, donkey, eel, ray, package, will, moon, heap, seep, fun.

Zebra, guitar, quick, jaw, box, vowel, monkey, eel, ray, package, fill, moon, heap, deep, sun.

Zebra, guitar, quick, lay, box, vowed, monkey, eel, ran, package, will, mojo, heap, seep, fun.

Zebra, guitar, quick, way, box, vowel, monkey, eel, raj, package, sill, moon, heap, deep, fun.

Zebra, guitar, quick, say, box, vowed, monkey, eel, raj, package, hill, moon, leap, weep, fun.

Zebra, guitar, quick, has, box, vowed, monkey, eel, ray, package, will, moon, leap, jeep, fun.

Can you find another?

Workings

Hint
In the word LOG, why might the L have be replaced with 50?

Answer
FO10.

Reasoning
If there is a Roman numeral, it is replaced by its modern equivalent.
   I = 1
   V = 5
   X = 10
   L = 50
   C = 100
   D = 500
   M = 1000

Double-Checking
CLICK = 100 50 1 100 K MILK  = 1000 1 50 K LOG   = 50 O G LIFE  = 50 1 F E ALIVE = A 50 1 5 E FOX   = F O 10

Workings

Hint
The answer is 4 digits long, so what must G equal?

Answer
423 + 675 = 1098.

Reasoning
Remembering that:
   even + even = even
   odd  + odd  = even
   even + odd  = odd

To discuss individual letters, it's easiest to represent the sum as:
   A B C
   D E F +
————————
 G H I J

A + D has to be over 9, which means that G = 1.

B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).

The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).

Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.

A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.

I is the only remaining odd number, so I = 9.

Which means that B = 2.

Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.

Therefore, A and D are 4 and 6 (but we don't yet know which is which).

Since the top row's digits have to add to 9, A can't be 6, so A = 4, making C = 3.

This makes the sum 423 + 675 = 1098.

Workings

Hint
What would happen in 36 hours?

Answer
7 hours and 12 minutes.

Reasoning
We can use a time that 12 hours and 18 hours both fit in to, in 36 hours:

   6 large pipes can drain 3 reservoirs.
   6 small pipes can drain 2 reservoirs.

Therefore, together, 6 large and 6 small pipes can drain 5 reservoirs.

36 hours ÷ 5 = 7.2 hours for one reservoir.

7.2 hours = 7 hours and 12 minutes for one reservoir.