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Puzzle 197
What is the smallest positive integer which, when multiplied by 7, gives an answer consisting of only 4's?
Hint
It will take a while to check 1 x 7, 2 x 7, 3 x 7. What do we know about the answer?
Answer
63,492 x 7 = 444,444
Reasoning
We can work backwards, as we know that the number multiplied by 7 has only 4's. We can try the following:
4 ÷ 7 ≈ 0.57 x
44 ÷ 7 ≈ 6.29 x
444 ÷ 7 ≈ 63.43 x
4,444 ÷ 7 ≈ 634.86 x
44,444 ÷ 7 ≈ 6,349.14 x
444,444 ÷ 7 = 63,492
At the recent interdepartmental jam making contest, four lucky candidates took part to make the juiciest strawberry jam.
As it happens, the person who came last was the oldest. Glen was three years older than the person who came second. Drew was neither the oldest nor the youngest. Emery finished ahead of the 27-year-old, but didn't win. Alex was also unlucky this time, and didn't win either.
The ages of the contestants were 24, 27, 30 and 32.
Can you work out who finished where, and how old they were?
After a local bank robbery, five suspects were interviewed.
Below is a summary of their statements.
Police know that each of them told the truth in one of the statements and lied in the other.
From this information, can you work out who committed the crime?
Billie said: It wasn't Chris It was Alex Drew said: It was Chris It wasn't Alex Chris said: It was Billie It wasn't Emery Alex said: It was Emery It wasn't Billie Emery said: It was Drew It was Alex