What’s it Worth? Each symbol has a numerical value. The total for the symbols is written at the end of each row and column. Can you find the missing total that should go where the question mark has been put?

In each group each of the letters A through H has one of the eight values listed. No two letters have the same value. The simple arithmetic problems are clues for determining the values of each letter. The three groups are independent. Group 1 2,5,6,8,10,13,15,21 H+D=G E-C=D H+G=A F+H=C E-F=G B+E=A Group 2 3,4,5,9,12,13,17,22 C-A=B H+D=A D+F=G F-A=E C-D=G Group 3 4,5,6,10,11,14,15,20 B-G=H A+E=C F-C=H D-B=A A+H=G E+F=D

In addition shown below, each of the letters A, B, C, D, and E represents one of the ciphers from 1 up to 5 (equal letters represent equal ciphers and different letters represent different ciphers). The first and last ciphers of the sum are given. A B C D E D A B E C E A A B C A C D A E ------------ + 9 C B A 0

Every alphabet represents a different digit from 1 to 9 to make the calculation. What are they?

P Q R S T U V W X 1. Each letter stands for one of the numbers 1 - 9. 2. S + Q = V and S is smaller than Q. 3. P = R + U. 4. In one of the diagonals, all 3 numbers are perfect squares. 5. In one of the two diagonals, (P, T, X or R, T, V) the 3 numbers are in ascending order when read from top to bottom, and each is evenly divisible by the same number, a number larger than 1. WHAT ARE THE NUMBERS? WHAT ARE THE NUMBERS? 9 5 2 3 4 7 8 6 1

The coloured shapes stand for eleven of the numbers from 0 to 12 The coloured shapes stand for eleven of the numbers from 0 to 12. Each shape is a different number. Can you work out what they are from the multiplications below? The upside down isosceles triangle is 0 because every time it is in a question it is the answer. The only number that rule applies to is 0. The diamond is 1 because every time it is in a question the other number in the question is the answer. This can only happen if the number is one. The square is 2 because something cubed is equal to something. All the numbers must be under twelve so the squares must be 2 or 1 because when those numbers are cubed, the answer is under twelve. It can't be 1 because 1 cubed is one and the answer was a different shape from the shape in the question. The semi-circle was 8 because 2 cubed is 8. The oval was 4 because the second question on the left hand row was 2 times the oval is 8 and 2 times 4 is 8. The circle is double the triangle because the rectangle times 4 is equal to the circle while the rectangle times 2 is equal to the triangle. Now we need to find a number and its double. It can't be 7 and 14 because all the numbers must be twelve or below. It can't be five and ten because the triangle and the circle are in sums which involve the 2 times tables and the 4 times tables and 5 isn't in any of them. It isn't 4 and 8 because the semi-circle and oval are those numbers and you can't have two different symbols which are the same number. It can't be 3 and 6 because they aren't in the 2 or 4 times table. It can't be 2 and 4 or 1 and 2 because all those numbers are other symbols. It also can't be 0 and 0 because they are different symbols so they must be different numbers. The only possible pair is 6 and 12 so the triangle is 6 and the circle is 12. The circle is 12 and the oval is 4 so 12 divided by 4 is the value of the rectangle. 12 divided by 4 is 3 so the rectangle is 3. The second sum on the top is rectangle times rectangle is equal to something. Since the rectangle is 3, it is 3 times 3 which is equal to 9. So the star with more sides is 9. That leaves the hexagon and the other star. It says 2 times star equals hexagon (see the second question on the right hand side) so we have to search for a pair of doubles. The only remaining pair of doubles under 12 is 5 and 10. http://nrich.maths.org/5714&part=