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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 565 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 49 (d) 58
  2. 2.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 180 (d) 60
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  4. 4.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 36 (d) 12
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 16 (d) 18
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 5 (d) 4
  8. 8.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 351 (c) 361 (d) 360
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  10. 10.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 553 (c) 543 (d) 440
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  12. 12.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 262 (c) 285 (d) 286
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 15 (d) 3
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 17 (d) 18
  16. 16.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 8 (c) 27 (d) 72
  17. 17.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 30 (d) 9
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 5 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 5 (b) 7 (c) 8 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  22. 22.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 54 (d) 51
  23. 23.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 23 (d) 69
  24. 24.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 144 (c) 48 (d) 16
  25. 25.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 182 (c) 181 (d) 172
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 5 (c) 6 (d) 4
  27. 27.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 106 (c) 115 (d) 124
  28. 28.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 316 (c) 315 (d) 282
  29. 29.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 229 (d) 228
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 6 (d) 5
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 17 (d) 6
  33. 33.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 18 (c) 162 (d) 54
  34. 34.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 186 (c) 176 (d) 194
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  36. 36.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 601 (b) 591 (c) 472 (d) 600
  37. 37.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 14 (c) 126 (d) 45
  38. 38.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
  39. 39.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 198 (c) 22 (d) 66
  40. 40.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 72 (c) 90 (d) 82

Answer key

  1. 49
  2. 60
  3. 9
  4. 36
  5. 8
  6. 17
  7. 5
  8. 360
  9. 7
  10. 552
  11. 6
  12. 285
  13. 4
  14. 14
  15. 17
  16. 24
  17. 27
  18. 5
  19. 2
  20. 7
  21. 5
  22. 51
  23. 69
  24. 48
  25. 181
  26. 5
  27. 115
  28. 315
  29. 228
  30. 6
  31. 3
  32. 17
  33. 54
  34. 185
  35. 4
  36. 600
  37. 42
  38. 258
  39. 66
  40. 81

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