Each letter represents a different digit from 0 to 9. Replace the letters of these nine words (rows: APE, PEA, LEI; LAW, AWL, PRO; PLY, LEG, AIR) by digits so that every row, column and diagonal of three numbers totals 1446. What number does AIR stand for? Answer with a natural number.
Eighteen disks hang by threads from a rod in six columns of three. Reading each column from top to bottom the numbers are: 3-7-8, 6-9-4, 2-4-5, 7-6-1, 8-1-3, 2-9-5 (the top disk of each column hangs from the rod; each lower disk hangs from the one above). Cut threads so that one set of numbers drops and nine disks still hang from the rod showing the numbers 1 to 9 once each. What is the least number of threads that must be cut? Answer with a natural number.
Three boards have these rows. Board 1 (top): 2 5 9 / 7 6 4 / 1 3 8. Board 2 (bottom left): 9 4 3 / 2 6 8 / 1 5 7. Board 3 (bottom right): 5 9 1 / 4 6 3 / 7 2 8. Circle a winning tic-tac-toe line (three in a row) on each board so that one board has a diagonal win, one a horizontal win and one a vertical win, and the nine circled numbers are 1 to 9 once each. Which board (1, 2 or 3) has the diagonal win? Answer with a natural number.
The numbers 49067 and 58132 are shown on two rows of blocks. Switch the positions of any two blocks so that one of the two new numbers is twice the other (neither starts with zero). What is the larger of the two new numbers? Answer with a natural number.
A sorcerer uses three symbols: the lightning bolt (L), the crescent moon (M) and the star (S), each with a fixed magical power. Six saucers form a ring. Top saucer: 1 bolt and 2 moons. Bottom saucer (opposite the top): 3 bolts and 4 stars. Upper right saucer: 2 bolts and 4 stars. Lower left saucer (opposite the upper right): 3 bolts and 1 moon. Lower right saucer: 1 star. The upper left saucer is empty. The three crossing arrows join opposite saucers and point to saucers of equal power. How many stars equal the power of one moon? Answer with a natural number.
Each letter stands for a different digit 0-9. Replace the letters so that every row, column and main diagonal of the 3x3 grid of words (BUG RUM GUN / OUR PUP MUD / TUB DUO NUT) totals 1515. What number is the word PUP? Answer with a natural number.
Each letter stands for a different digit 0-9. Replace the letters so that every row, column and main diagonal of the 3x3 grid of words (ORB TIP PIT / PEE ORA TWO / TOW POD OAR) totals 1167. What number is the word ORA? Answer with a natural number.
Eight numbers are arranged around a ring, clockwise from the top left: 46, ?, 64, 37, 82, 55, 100, 73. What number replaces the question mark? Answer with a natural number.
Each line and symbol in the four outer circles is transferred to the centre circle by the rules: appearing once, it is transferred; twice, it is possibly transferred; three times, it is transferred; four times, it is not transferred. Which circle A to E should be at the centre? Choose from the options labelled in the figure.
