Hint: These are the first letters of the words: P, B, D, L, O, A, B, H, S, B.
pro + nou + nce = pronounce
bea + uti + ful = beautiful
dim + ens + ion = dimension
liv + est + ock = livestock
ope + rat + ion = operation
ann + oun + cer = announcer
bed + spr + ead = bedspread
hou + seb + oat = houseboat
sev + ent + een = seventeen
bre + akf + ast = breakfast
The BrainBashers mechanical computer is a very sensitive device, in consists of four sequential cog wheels which are in constant mesh.
The largest cog has 63 teeth and the others have 42, 35 and 27 respectively.
By accident, Daniel started to rotate the largest cog.
How many revolutions must he rotate the largest cog make before the computer is back in its starting position with all of the cogs where they started?
Hint: Try breaking each cog size into prime factors.
Answer: 30 revolutions.
If we break each wheel into its prime factors, we get:
63 = 3 x 3 x 7
42 = 2 x 3 x 7
35 = 5 x 7
27 = 3 x 3 x 3
We now think of rotating the large wheel just once, and this is 3 x 3 x 7 teeth moved (3 x 21), and we can see that 42 tooth wheel also has a 3 x 7 (21 teeth) in it, with an extra 2. If we therefore rotate the 63 toothed wheel twice, the 42 will have rotated three times.
The answer involves cancelling any common factors from the large wheel. We can cancel 3, 3, 7 from any of the smaller ones to leave 2 (from the 42), 5 (from the 35) and 3 (from the 27). 2 x 5 x 3 = 30. QED.
Below are ten words, from each word, remove a single letter and rearrange the remaining letters to find ten new words which are related to each other.
ENERGY - Y = GREEN
DOORMAN - D = MAROON
CLEAREST - E = SCARLET
WEIGHT - G = WHITE
OUTLIVE - U = VIOLET
EMBARK - K = AMBER
CALMER - L = CREAM
SOLEMN - S = LEMON
VOIDING - V = INDIGO
ARCHERY - A = CHERRY
My friend, Alex, struggles a little. I recently asked him to buy me some ribbon for my daughter's pretty pink bonnet.
He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches.
When I measured the resulting ribbon I only had 5÷8 of the length I required.
I asked for 7 feet, 4 inches and my friend brought me 4 feet, 7 inches.
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:
(5 ÷ 8) x (12 x A + B) = (12 x B + A)
A = (91 ÷ 52) x B
As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet. B = 4 is the only possible value, which means that A = 7. So I originally asked for 7 feet, 4 inches. QED.
By changing the second letter of each word below, you can make another valid word. Can you change each word such that the second letters will reveal an eleven letter word when read downwards. Therefore, what now reads AWPYRNUCEPA will be a real word.