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#154 Party line-up

“So, Maureen, how electable are they?” asked Tariq, the local party chairperson, counting up the number of people on the list of possible candidates for the by-election.

“It’s good news and bad news. The good news is that I have looked into their backgrounds and discovered that eight of them have proven leadership skills, seven of them have been completely honest about their expenses, and six of them are always loyal to the party when they tweet.”

“Good. And because I know how many candidates there are, I can be certain that at least one of them must have all three of these virtuous traits! What’s the bad news?”

“Um, well you are right, but unfortunately there is only one candidate who has all three virtues – and it is your nemesis Judy Prim.”

How many candidates are there in total?

Solution next week

#153 Tightwad’s safe

Solution

The safe code is 9075461328. The key clue is that the digits 0 to 9 are all used along the top and side of the grid. 0 times anything is 0, so the second column must all be 0s. One times anything can only have one digit, so the only place for 1 is the second row. Two times any single digit is even and is less than 20, so the only place left for 2 is the fourth row. And since three times something is less than 30, the third row is the only place left for 3. So 5 must be the fourth column since one of the numbers ends in 5. Similar logic leads to all of the other digits.