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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 915 · 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 10? (a) 11 (b) 10 (c) 9 (d) 8
  2. 2.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) 33 (b) 90 (c) 10 (d) 30
  3. 3.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 76 (c) 67 (d) 68
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 9 (b) 18 (c) 17 (d) 15
  5. 5.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 498 (c) 410 (d) 507
  6. 6.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 162 (c) 161 (d) 152
  7. 7.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 480 (d) 471
  8. 8.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) 21 (b) 18 (c) 54 (d) 6
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 17 (d) 6
  10. 10.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 618 (d) 619
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  12. 12.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 159 (c) 168 (d) 160
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  14. 14.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 175 (c) 184 (d) 166
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  16. 16.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 528 (c) 529 (d) 519
  17. 17.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 381 (c) 391 (d) 390
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 5 (d) 4
  19. 19.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) 27 (c) 72 (d) 8
  20. 20.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 553 (d) 552
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  22. 22.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 387 (d) 336
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 3 (b) 4 (c) 6 (d) 5
  24. 24.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 498 (c) 640 (d) 630
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  26. 26.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) 20 (b) 63 (c) 180 (d) 60
  27. 27.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 288 (c) 264 (d) 289
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 8 (c) 9 (d) 7
  30. 30.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 314 (c) 354 (d) 364
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  33. 33.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 216 (c) 324 (d) 207
  34. 34.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) 69 (b) 72 (c) 207 (d) 23
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 5 (d) 16
  36. 36.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) 144 (b) 48 (c) 16 (d) 51
  37. 37.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 356 (c) 427 (d) 417
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 4 (d) 2
  39. 39.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 489 (c) 398 (d) 490
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7

Answer key

  1. 9
  2. 30
  3. 67
  4. 17
  5. 507
  6. 161
  7. 480
  8. 18
  9. 17
  10. 618
  11. 4
  12. 159
  13. 2
  14. 175
  15. 8
  16. 528
  17. 390
  18. 6
  19. 24
  20. 552
  21. 5
  22. 396
  23. 5
  24. 639
  25. 6
  26. 60
  27. 288
  28. 4
  29. 8
  30. 363
  31. 3
  32. 8
  33. 216
  34. 69
  35. 16
  36. 48
  37. 426
  38. 4
  39. 489
  40. 7

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