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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 396 · 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 5? (a) 4 (b) 5 (c) 6 (d) 10
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  3. 3.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 124 (c) 133 (d) 142
  4. 4.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 351 (c) 352 (d) 342
  5. 5.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 134 (d) 143
  6. 6.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) 30 (b) 10 (c) 33 (d) 90
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  8. 8.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 96 (c) 104 (d) 86
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 16 (b) 5 (c) 15 (d) 17
  10. 10.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 376 (c) 457 (d) 447
  11. 11.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 492 (d) 631
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  14. 14.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) 51 (c) 153 (d) 54
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  16. 16.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 162 (c) 144 (d) 153
  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) 30 (c) 27 (d) 9
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 5 (d) 14
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 4 (d) 15
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  21. 21.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 535 (c) 534 (d) 525
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 18 (d) 8
  24. 24.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 173 (c) 182 (d) 164
  25. 25.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 603 (d) 613
  26. 26.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 314 (c) 354 (d) 363
  27. 27.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 150 (c) 142 (d) 141
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  29. 29.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 119 (d) 110
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 18 (d) 20
  31. 31.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 276 (c) 267 (d) 256
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  34. 34.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 516 (d) 507
  35. 35.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 476 (c) 597 (d) 607
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 13 (d) 14
  37. 37.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) 7 (b) 24 (c) 63 (d) 21
  38. 38.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) 161 (c) 162 (d) 152
  39. 39.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 75 (d) 84
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18

Answer key

  1. 5
  2. 20
  3. 133
  4. 351
  5. 143
  6. 30
  7. 2
  8. 95
  9. 16
  10. 456
  11. 630
  12. 2
  13. 5
  14. 51
  15. 3
  16. 153
  17. 27
  18. 6
  19. 15
  20. 9
  21. 534
  22. 9
  23. 18
  24. 173
  25. 612
  26. 363
  27. 141
  28. 3
  29. 119
  30. 19
  31. 276
  32. 7
  33. 7
  34. 516
  35. 606
  36. 14
  37. 21
  38. 161
  39. 75
  40. 17

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