Welcome to Ian’s Friday Puzzle! Dust off those Friday cobwebs with a little manipulation of the old grey matter. Perplexing puzzles, logical, illogical, and sometimes just plain stupid. Be prepared to be bewildered, befuddled and bedazzled!
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Which numbers, less than 100, are the product of exactly three different prime factors?
The electricity has gone out and Beth and Keith are getting dressed in the dark.
Beth has 6 yellow socks and 8 black socks in her drawer.
She wants two of the same colour.
How many will she have to take out to guarantee a matching pair?
Keith has 6 black socks, 8 blue socks and 4 green socks in his drawer.
He wants to wear socks that don’t match.
How many will he have to take out to guarantee that a pair that don’t match?
Keith and his sons William and Robbie have the same birthday.
Today Keith is 32, William is 4 and Robbie is 1.
How old will Keith be when his age is the sum of the ages of William and Robbie?
I have five whole numbers.
The mean of the numbers is 4, the median 3,
the mode is 1 and the range is 9.
What are my five numbers?
After a huge party there are 150 dishes to be washed by hand.
Chris says he can do it in 50 minutes.
Danny says he is slower and would take 1¼ hours.
As there are two sinks they decide to do it together.
How long will it take them and how many dishes each would they wash?
My combination lock has 4 dials, each dial has the numbers 1, 2, 3 and 4 on it.
To open the lock, no number can be repeated in the 4 digit code.
How many different combinations are there to open the lock?
If all the different combinations were added up, what would be the total?
A cyclist cycles up a hill and then down again.
The route is exactly 1 km to the top of the hill.
He wants to cycle at an average speed of 15 km/h.
If he can cycle up the hill at an average speed of 10 km/h at what speed must he come down the hill?
I have started playing ten pin bowling.
In my last game I bowled 199 and this raised my average (mean) from 177 to 178.
I want to raise my average to 179.
What must I bowl in my next game?
I have a four digit number with no zeros.
The second digit is four more than the first and three times the third digit.
The third digit is two more than the last and two less than the first digit.
The first digit is five times the last digit.
What number do I have?
Tessa the teacher has three cards with different numbers on them.
She says, ‘The numbers on the three cards add to a square number’.
She peeks at two of the three cards and says, ‘these two numbers add to a square number’.
She peeks at two different cards of the three and says, ‘these two numbers also add to a square number’.
She peeks at two different cards of the three and says, ‘These two numbers don''t add to a square! It''s either 5 too little or 6 too big!"
What are the three numbers on the cards?