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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 353 · 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 times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
  2. 2.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 192 (c) 202 (d) 201
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  7. 7.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 178 (c) 160 (d) 169
  8. 8.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 376 (c) 366 (d) 322
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 6 (d) 15
  10. 10.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) 33 (c) 90 (d) 10
  11. 11.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) 7 (c) 21 (d) 63
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 18 (d) 8
  14. 14.The numbers 1 to 9 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) 18 (c) 5 (d) 15
  15. 15.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 480 (c) 612 (d) 603
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 18 (d) 19
  17. 17.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 402 (c) 495 (d) 486
  18. 18.The numbers 7 to 15 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) 36 (c) 11 (d) 99
  19. 19.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 333 (c) 324 (d) 334
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 17 (c) 7 (d) 16
  21. 21.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) 216 (b) 72 (c) 24 (d) 75
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 8 (d) 19
  23. 23.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) 14 (c) 42 (d) 126
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 14 (c) 12 (d) 13
  25. 25.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 234 (c) 351 (d) 243
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 2 (d) 4
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 17 (b) 19 (c) 7 (d) 18
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 4 (b) 2 (c) 5 (d) 3
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 7 (b) 6 (c) 9 (d) 8
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 17 (d) 5
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 19 (d) 9
  32. 32.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 174 (c) 184 (d) 183
  33. 33.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 387 (c) 396 (d) 336
  34. 34.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) 27 (b) 81 (c) 30 (d) 9
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 3 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 9 (b) 13 (c) 11 (d) 14
  38. 38.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 355 (c) 308 (d) 345
  39. 39.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) 6 (b) 54 (c) 18 (d) 21
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 14 (b) 5 (c) 13 (d) 15

Answer key

  1. 18
  2. 201
  3. 8
  4. 3
  5. 5
  6. 7
  7. 169
  8. 375
  9. 16
  10. 30
  11. 21
  12. 2
  13. 18
  14. 15
  15. 612
  16. 18
  17. 495
  18. 33
  19. 333
  20. 17
  21. 72
  22. 19
  23. 42
  24. 13
  25. 243
  26. 3
  27. 18
  28. 4
  29. 8
  30. 16
  31. 19
  32. 183
  33. 396
  34. 27
  35. 4
  36. 8
  37. 13
  38. 354
  39. 18
  40. 14

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