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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 943 · 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 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 360 (c) 318 (d) 370
  2. 2.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 390 (c) 399 (d) 400
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 19 (d) 20
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 8 (d) 7
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 5 (b) 6 (c) 4 (d) 7
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 15 (c) 4 (d) 16
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  8. 8.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) 30 (c) 27 (d) 9
  9. 9.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 457 (c) 456 (d) 447
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 17 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 16 (d) 15
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  14. 14.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 236 (c) 247 (d) 246
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 7 (c) 8 (d) 9
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 4 (b) 7 (c) 6 (d) 5
  17. 17.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 346 (c) 412 (d) 402
  18. 18.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 195 (c) 196 (d) 202
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 15 (d) 17
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 16 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  22. 22.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) 24 (b) 72 (c) 75 (d) 216
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 5 (d) 4
  25. 25.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 168 (d) 150
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 3 (d) 2
  27. 27.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 438 (d) 429
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  30. 30.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 116 (c) 125 (d) 126
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  33. 33.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 588 (c) 579 (d) 589
  34. 34.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) 54 (b) 17 (c) 153 (d) 51
  35. 35.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 124 (d) 123
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 7 (d) 17
  37. 37.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 249 (c) 240 (d) 238
  38. 38.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 192 (c) 201 (d) 206
  39. 39.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 640 (c) 639 (d) 630
  40. 40.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) 198 (b) 22 (c) 66 (d) 69

Answer key

  1. 369
  2. 399
  3. 19
  4. 7
  5. 6
  6. 15
  7. 4
  8. 27
  9. 456
  10. 17
  11. 3
  12. 15
  13. 9
  14. 246
  15. 8
  16. 6
  17. 411
  18. 195
  19. 16
  20. 17
  21. 3
  22. 72
  23. 8
  24. 5
  25. 159
  26. 4
  27. 438
  28. 6
  29. 7
  30. 125
  31. 6
  32. 17
  33. 588
  34. 51
  35. 123
  36. 17
  37. 249
  38. 201
  39. 639
  40. 66

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