Games: While Santa sleeps ...

Here are a few brainteasers from Chris Maslanka to challenge your wits. The answers appear below - so don't look if you really want to sharpen your skills. Illustrations by Kate Smiley.

Q1: Santa is taking forty winks before loading up his sleigh. His "microsleep" alarm clock is set to go off at eight. At the moment the big hand and the little hand are both exactly on minute divisions, with the big hand exactly four minutes ahead of the little hand.

How long will it be before his alarm clock goes off?

Q2:The measuring cylinders Ms Frangipani's had ordered through a mail order firm has been delayed in the post, so she has to make her belated Christmas cake using her two old measuring cylinders. One of these measures 3 fluid ounces and the other measures 10 fluid ounces. The trouble is she needs to measure out exactly 8 fluid ounces of brandy. Ms Frangipani is not about to cheat as she is most particular, punctilious and pedantic, some would even say pernickety.

How can she do it?

Q5: It's not just at the North Po1e that things are chaotic. All over the world postpersons are being puzzled by the cryptic messages Santa's helpers have written on the parcels. Take this one, currently puzzling Freda, and destined for a Mr Fermat somewhere on Christmas Crescent:

To the only house on Christmas Crescent which is one more than a perfect square and one less than a perfect cube.

Now Freda had been to college and knew that a square was a whole number multiplied by itself, for example: 4 = 2 X 2 or 100 = 10 X 10. She also knew that a perfect cube was a whole number times itself times itself; for example: 64 is a perfect cube because 4 X 4 X 4 = 64; so is 125 as 5 X 5 X 5 = 125.

To which of the houses should Freda deliver Mr Fermat's package?

Q6: Because of the chaos reigning in Santa's Grotto, people that do receive presents from Santa this year may well get the wrong things.

Ben has asked Santa for a car inner-tube but is getting a model car crammed into a tube.

Sir Humphrey Poshboy, on the other hand, has asked for a model car and has even left an imperious message to that effect on Santa's answering machine. Will he be surprised when he receives some paper for a fax machine!

Ivor Greenfinger has asked for something to water the garden with but is going to get some garden implements instead. Mind you he's lucky not to be getting a pair of tights!

Explain these seasonal misunderstanding and help set things straight.

Q3: In his dreams Santa sees a number of shepherds and sheep about to be startled by angels. By counting he finds there to be 84 legs in all. If the sheep were to become shepherds and the shepherds sheep, there would have been only 48 legs.

How many shepherds were there and how many sheep?

Q4 While Santa sleeps and the shepherds watch their flocks, an angel is towing a star into position above a little-known stable in Nazareth. When they spy it the three wise men began to argue. Does it contain more triangles than quadrilaterals (four-sided figures)?

Can you settle this burning question for them once and for all so that they can get back to the true message of Christmas?

Q7: Over in Santa's workshop Ann Droid is already stacking up the parcels according to her own peculiar logic. Because of a programming fault this takes the following form: -

With the exception of the numbers on the bottom row, the number on every parcel has to equal the sum of the numbers on the two parcels below it.

The numbers in the second row up are all odd digits.

No number in the stack may end in zero.

Every number must be a whole number greater than zero.

So far the trusty robot has managed to put a number I in the bottom left parcel.

Can you help her to fill in the missing numbers before she blows a fuse? solutions

1 The clock now shows 8:48, so he has only 11 hours 12 minutes to go.

2 Fill the smaller container and tip it into the larger container. Do this a total of three times. This leaves 2 in the little container. Empty the large container back into the brandy bottle. Pour the 2 fluid ounces into the large container. Then fill the small container twice, each time tipping the contents into the larger container. It now contains 3 + 3 + 2 = 8 fluid ounces.

3 There are 2 shepherds and 20 sheep. This makes 84 legs. if there were 20 shepherds and 2 sheep, they'd have 48 legs.

4 There are 10 triangles all together: A, B, C, D & E and 5 of the form AFC. There are 10 ordinary-shaped quadrilaterals: 5 "kites" of the form AF (these are convex), and 5 "paper darts" of the form AFDC (these are partially concave). There are also 5 "bow-ties"- in which the lines cross over- as in AB. If you count these, there are more quadrilaterals than triangles. If not, there are the same number of each.

5 No. 26 is the only possibility.

6 Ben had wanted a car inner-tube but got a car in a tube. Sir Humphrey Poshboy wanted a facsimile rolls but got facsimile rolls. Ivor Greenfinger asked for some hose. He will receive some hoes, but is lucky not to be receiving some hose!

7 This is how the boxes should be stacked: