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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 192 · 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 12? (a) 6 (b) 13 (c) 7 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  3. 3.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) 63 (b) 180 (c) 20 (d) 60
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  5. 5.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 426 (c) 362 (d) 436
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 17 (b) 16 (c) 7 (d) 18
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 17 (c) 16 (d) 5
  8. 8.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 112 (c) 120 (d) 111
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 14 (b) 3 (c) 13 (d) 15
  10. 10.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 288 (c) 325 (d) 315
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 5 (d) 2
  12. 12.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) 8 (b) 27 (c) 72 (d) 24
  13. 13.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 140 (c) 150 (d) 158
  14. 14.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 429 (c) 420 (d) 358
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 7 (d) 17
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 15 (d) 17
  17. 17.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 306 (c) 351 (d) 342
  18. 18.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) 9 (c) 27 (d) 30
  19. 19.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 105 (d) 96
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  21. 21.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 186 (d) 177
  22. 22.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) 153 (c) 162 (d) 144
  23. 23.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 283 (c) 273 (d) 260
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 2 (d) 5
  26. 26.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 54 (c) 57 (d) 18
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 21 (b) 20 (c) 19 (d) 9
  28. 28.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 466 (c) 592 (d) 591
  29. 29.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 520 (c) 418 (d) 519
  30. 30.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 432 (c) 441 (d) 366
  31. 31.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) 63 (b) 66 (c) 21 (d) 189
  32. 32.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 516 (c) 517 (d) 416
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  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) 51 (c) 153 (d) 17
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 18 (d) 16
  37. 37.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  38. 38.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 238 (c) 237 (d) 228
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 7 (c) 10 (d) 13
  40. 40.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) 11 (c) 99 (d) 36

Answer key

  1. 7
  2. 6
  3. 60
  4. 5
  5. 435
  6. 17
  7. 16
  8. 111
  9. 14
  10. 324
  11. 4
  12. 24
  13. 149
  14. 429
  15. 17
  16. 16
  17. 351
  18. 27
  19. 105
  20. 6
  21. 177
  22. 153
  23. 282
  24. 3
  25. 4
  26. 54
  27. 20
  28. 591
  29. 519
  30. 441
  31. 63
  32. 516
  33. 8
  34. 51
  35. 19
  36. 17
  37. 9
  38. 237
  39. 12
  40. 33

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