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Puzzle 101
Below, 9 nine-letter words have been broken into chunks of three letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 9 words are?
ome clo ere ref int ere
bar ple pin ise phy gra
hni bio ewh eap sor fes
tec ckw som que tpr pro
nce ter foo
Answers
foo + tpr + int = footprint
som + ewh + ere = somewhere
pin + eap + ple = pineapple
tec + hni + que = technique
ref + ere + nce = reference
pro + fes + sor = professor
bio + gra + phy = biography
clo + ckw + ise = clockwise
bar + ome + ter = barometer
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Puzzle 102
Can you find a five-digit number that has no zeros nor ones in it and no digit is repeated, where:
The fourth digit is a quarter of the total of all of the digits.The second digit is twice the first digit.The third digit is the largest.The 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 103
Below you will find 15 well-known seven-letter words, with only their endings remaining.
Can you find the words? ----nst----nip----fth----rno----dox----sil----nac----iem----arb----ior----bey----van----ipt----dth----nox
Reverse each group of 4 letters:
MOOT CYNA SKOO IOPS EHTL TORB YCBH
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
