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.
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Puzzle 132
Using the clues from below can you find ten words?
Once you have placed the words into the correct order you will find that each word is different from the previous word by only one letter.
For example, DOG may be followed by DIG, etc.
in the back of the netsock materialforestbaby horsehooded robespiral of wirenot hotroasting metalearthy groundnot bad
Hint
'in the back of the net' begins with the letter G.
Answers
good = not bad
wood = forest
wool = sock material
cool = not hot
cowl = hooded robe
coil = spiral of wire
soil = earthy ground
foil = roasting metal
foal = baby horse
goal = in the back of the net
