Below, 10 nine-letter words have been broken into chunks of three letters.
These chunks have been mixed up, no chunk is used twice, and all of the chunks are used.
Can you determine the 10 original words?
rbr tim sag tel lig ent
hea dli ble whi htn fer
car age esc ing ind wat
til hai ush dif eta new
rlw all erf ope ent ght
Hints
The first letters of the words are: T, T, H, D, W, L, H, W, C, N.
Answers
tel + esc + ope = telescope
tim + eta + ble = timetable
hai + rbr + ush = hairbrush
dif + fer + ent = different
wat + erf + all = waterfall
lig + htn + ing = lightning
hea + dli + ght = headlight
whi + rlw + ind = whirlwind
car + til + age = cartilage
new + sag + ent = newsagent
??
Puzzle 4
Can you find a five-digit number that has no zeros, no ones, no digit is repeated, and:
the fourth digit is a quarter of the total of all of the digitsthe second digit is twice the first digitthe third digit is the largestthe last digit is the sum of the first two digits
Reasoning
We can start by labelling the digits as ABCDE.
We know that:
(i) B = 2 x A
and:
E = A + B
And using (i) we get:
E = A + (2 x A) (ii) E = 3 x A
If A = 1, this isn't allowed (as there are no 1's in the puzzle).
If A = 2, then B = 4, and E = 6.
If A = 3, then B = 6, and E = 9, but this isn't allowed (as C has to be the largest digit).
So, A = 2, B = 4, E = 6, and we now have to find C and D.
We also know that:
D = (A + B + C + D + E) ÷ 4
And using (i) and (ii) we get:
D = [A + (2 x A) + C + D + (3 x A)] ÷ 4
so:
3 x D = (6 x A) + C
so:
(iii) D = [(6 x A) + C] ÷ 3
C can only be 7, 8 or 9 (as it's the largest digit, and we've already found 6) and (iii) tells us that it must be a multiple of 3, which means that C = 9. Leaving D = 7.
So the final number is: 24976.
Double-Checking
The answer is 24976.
The fourth digit is a quarter of the total of all of the digits.
A + B + C + D + E = 2 + 4 + 9 + 7 + 6 = 28, and 28 ÷ 4 = 7.
The second digit is twice the first digit.
4 = 2 x 2.
The third digit is the largest.
9 is the largest digit.
The last digit is the sum of the first two digits.
6 = 2 + 4.
