You see a design for a stained glass window which consists of a large circle and four small circles symmetrically placed within the larger as shown. The four smaller circles touch the outer circle and also meet at its centre.
The four "petals" labelled Y are in yellow glass, the four parts labelled B are in blue and the four parts labelled R are red.
We know there will be a total of 400 square centimetres of yellow glass in the window. Do you know how much blue glass is needed and how can you be sure?
We need at least seven 4s to write the number 100 as a sum of numbers made up of the digit 4:
44 + 44 + 4 + 4 + 4 = 100
We need at least sixteen 4s to make 1,000:
444 + 444 + 44 + 44 + 4 + 4 + 4 + 4 + 4 + 4 = 1,000
Now, what is the smallest number of 4s we need to represent 1,000,000 in this way?
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Four identical dice are piled as shown in the picture. There are dots on the faces. How many dots are there on the bottom face of the bottom-most one? How can one guess? The sum of the opposite faces of real dice is *usually* 7. But you cannot rely on this fact in this problem. |
Professor Tomus has a great collection of books. The way Tomus numbers
his book collection speaks volumes about his eccentricity:
8, 15, 22, 29, 36, 43... and so on up to 711117.
If these books were set out on one long shelf in numerical order, what would be the number on the spine of the middle volume?
Garabaggio's Square is made up of a small number of squares fitted together without gaps or overlap to make a rectangular canvas measuring 176 cm by 177 cm. The side of each square measures a whole and different number of centimetres. The square at the top left measures 41 cm by 41 cm; the one at the bottom right measures 99 cm by 99 cm. Can you deduce the measurements of all the others?
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so that the first part multiplied by 4, the second part divided by 4, the third part plus 4, and the fourth part minus 4, all equal the same number. |
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Start calculating!
| 405 | Take a three-digit number
and add it to another number made by rearranging the
three digits of the number you took. The sum of these two
numbers can, in its turn, also be made by rearranging the
same three digits. The example shown is inadmissible because we don't normally write a number with a zero at the beginning. There is another solution without this shortcoming. Can you find it? |
| 045 + | |
| 450 |
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B * ( A+C+D+E+F ) = 225 C * ( A+B+D+E+F ) = 301 D * ( A+B+C+E+F ) = 369 E * ( A+B+C+D+F ) = 400 F * ( A+B+C+D+E ) = 525 |
The next problem is: Solve for A, B, C, D, E, and F. Find integer values. |
A very rich farmer was getting bored and decided to count his horses. After counting them he discovered that the number of horses could be divided by 2,3,4,5,6,7,8,9 and 10. What is the MINIMUM number of horses this farmer has?
Alphametics or Cryptarithems
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