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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 459 · 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.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 14 (b) 16 (c) 5 (d) 15
  3. 3.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) 22 (b) 198 (c) 69 (d) 66
  4. 4.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) 17 (b) 153 (c) 54 (d) 51
  5. 5.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) 9 (b) 27 (c) 30 (d) 81
  6. 6.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 21 (d) 54
  7. 7.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 216 (d) 75
  8. 8.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 66 (c) 189 (d) 63
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  10. 10.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 186 (c) 196 (d) 195
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 7 (b) 10 (c) 8 (d) 11
  12. 12.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 247 (c) 246 (d) 237
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  14. 14.The numbers 3 to 11 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) 21 (c) 63 (d) 7
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 9 (d) 20
  16. 16.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 135 (c) 48 (d) 15
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 7 (b) 6 (c) 8 (d) 5
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  20. 20.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 454 (c) 444 (d) 453
  21. 21.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
  22. 22.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) 285 (c) 286 (d) 262
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  24. 24.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) 229 (c) 224 (d) 228
  25. 25.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 382 (c) 372 (d) 326
  26. 26.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) 72 (b) 27 (c) 24 (d) 8
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 2 (c) 3 (d) 5
  28. 28.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 30 (c) 90 (d) 33
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 7 (d) 18
  30. 30.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 250 (c) 267 (d) 258
  31. 31.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 470 (c) 598 (d) 588
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 4 (d) 1
  33. 33.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) 45 (b) 42 (c) 14 (d) 126
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 4 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  37. 37.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
  38. 38.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 213 (c) 223 (d) 220
  39. 39.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 324 (c) 294 (d) 333
  40. 40.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 264 (c) 279 (d) 288

Answer key

  1. 3
  2. 15
  3. 66
  4. 51
  5. 27
  6. 18
  7. 72
  8. 63
  9. 8
  10. 195
  11. 10
  12. 246
  13. 2
  14. 21
  15. 20
  16. 45
  17. 7
  18. 17
  19. 20
  20. 453
  21. 39
  22. 285
  23. 7
  24. 228
  25. 381
  26. 24
  27. 4
  28. 30
  29. 18
  30. 267
  31. 597
  32. 3
  33. 42
  34. 5
  35. 5
  36. 8
  37. 57
  38. 222
  39. 333
  40. 288

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