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March 2001 - Nobody has yet submitted the correct solution to this problem. You can still send in your solution.

November 2000 - The solution to this problem does not lend itself to an HTML document. If you want to know the answer and can accept an Excel spreadsheet as an e-mail attachment please use the form above.

June 2001 - Nobody has yet submitted the correct solution to this problem. You can still send in your solution.

July 2001 - Nobody has yet submitted the correct solution to this problem. You can still send in your solution.

September 2001 - Nobody has yet submitted the correct solution to this problem. You can still send in your solution.

Solution to the August 2000 Brain Teaser

No.1                    No.2      No.3    No.4

Neither No.1 nor No.2 can see any caps at all. Therefore they would not be able to work out the colour of their own caps.

No. 4 can see the caps of No.2 and No.3. If No.2 and No.3 had the same colour caps, he would know that his own cap was the other colour and therefore he would have shouted out the colour of his cap.

The fact that No.4 didn't shout out immediately tells No.3 that his cap is different to the colour of No.2's cap. He can see the colour of No.2's cap and therefore he knows the colour of his own cap and shouts out accordingly.

SOLUTION TO THE DECEMBER 2000 BRAIN TEASER

Turn on two of the three switches and leave on for a few minutes. Then turn one of the switches off. Go upstairs. The switch that you left on controls the light bulb that is still on. The other two light bulbs will be switched off. Feel these light bulbs. The third switch that you did not turn on controls the light bulb that is cold. The other light bulb will still be warm and is controlled by the switch you turned on and then off.

SOLUTION TO THE JANUARY 2001 BRAIN TEASER

The sender puts the valuable item in the box and attaches his padlock through the hasp. He sends the box to his friend who attaches his own padlock through the hasp too. His friend sends the box back to the sender, who removes his own padlock and returns the box, with his friend's padlock still attached, to his friend. The friend unlocks his padlock and removes the valuable item.

SOLUTION TO THE FEBRUARY 2001 BRAIN TEASER

The eight ways in which you can make three different positive integers, each less than ten, add up to 15 is shown below:

8+6+1 9+5+1

7+6+2 8+5+2 9+4+2

8+4+3 7+5+3 6+5+4.

There are four solutions containing the integer 5, three solutions containing the integers 2,4,6 or 8 and two solutions containing the integers 1, 3, 7, or 9.

The number in the central square of the grid must feature in four of the solutions: one vertical line, one horizontal line and two diagonal lines. Therefore the central square must contain the integer 5.

The integers in the corner squares feature in three solutions: one vertical, one horizontal and one diagonal. There are four corner squares and four integers which appear three times in solutions. Therefore the corner squares contain the integers 2, 4, 6 and 8.

The numbers in the squares between the corner squares feature in only two solutions: one vertical and one horizontal. There are four such squares and four such numbers: 1,3,7 and 9.

Having placed one integer in a corner square, the number in the opposite corner is determined by the fact that the sum of the diagonal is 15. The remaining two corner numbers can be placed in either of two positions but there is only one solution because rotation of any one arrangement of the integers, about a diagonal line, will produce the other arrangement. Having placed the corner integers, the positions of the remaining integers are fixed. Again there is only one solution, because rotation about a perpendicular axis through the center of the grid will yield all the possible arrangements of the integers.

SOLUTION TO THE APRIL 2001 BRAIN TEASER

It is fairly easy to work out those years where the weekdays are the same for each month as they were in 2001. The years where this is the case are:

2007, 2018, 2029, 2035, 2046, 2057, 2063, 2074 ...

The days of the first full moon after the vernal equinox for these years are:

1st April, 27th March, 23rd March, 16th. April, 12th. April ...

The first year in which Easter falls on 15th April is therefore 2046 and the calendars would have to be stored for 45 years.

SOLUTION TO THE MAY 2001 BRAIN TEASER

If the number of camels sold is C, then the unit selling price for each camel is also C. The proceeds of the sale are C.C silver coins.

If the purchase prices of a goat and a dog are G and D respectively, then G + D = 10 and C.C = 10.(2N-1) + G where N is an integer greater than zero.

Hence C.C = 20.N - D, where C is an integer and D is an integer less than ten. Further N > 5 since a camel costs more than a sheep.

There are a number of solutions for (C,G,D):

(C,G,D) = (14,6,4) or (16,6,4) or (24,6,4) or (26,6,4) or (34,6,4) or (36,6,4)... etc., but the cost of a dog is 4 silver coins in each solution.

SOLUTION TO THE AUGUST 2001 BRAIN TEASER

October 2000 - The solution submitted by Christopher George Pereira is:

                       where T = 1, R = 5, Y = 3 then 113 * 153 = 153 *113 = THINK = 17289