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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 350 · 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 4? (a) 3 (b) 4 (c) 5 (d) 10
  3. 3.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) 21 (c) 7 (d) 63
  4. 4.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) 14 (b) 45 (c) 126 (d) 42
  5. 5.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) 75 (b) 24 (c) 216 (d) 72
  6. 6.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 176 (c) 184 (d) 175
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 18 (d) 19
  8. 8.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) 69 (c) 22 (d) 66
  9. 9.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) 27 (b) 72 (c) 8 (d) 24
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  13. 13.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) 23 (b) 72 (c) 69 (d) 207
  14. 14.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 14 (d) 15
  16. 16.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) 60 (d) 20
  17. 17.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 420 (c) 352 (d) 411
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 10 (b) 9 (c) 7 (d) 8
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 10 (d) 11
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 7 (b) 5 (c) 6 (d) 8
  21. 21.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 134 (c) 144 (d) 152
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 15 (b) 14 (c) 4 (d) 16
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  25. 25.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 182 (c) 181 (d) 172
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  30. 30.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 264 (c) 248 (d) 255
  31. 31.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
  32. 32.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 170 (c) 160 (d) 178
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 5 (b) 4 (c) 6 (d) 3
  34. 34.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 459 (d) 460
  35. 35.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 50 (c) 32 (d) 41
  36. 36.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 262 (c) 261 (d) 246
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  38. 38.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) 183 (d) 184
  39. 39.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 97 (c) 98 (d) 106
  40. 40.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) 90 (d) 33

Answer key

  1. 7
  2. 4
  3. 21
  4. 42
  5. 72
  6. 175
  7. 19
  8. 66
  9. 24
  10. 17
  11. 3
  12. 4
  13. 69
  14. 53
  15. 15
  16. 60
  17. 420
  18. 9
  19. 11
  20. 7
  21. 143
  22. 17
  23. 15
  24. 3
  25. 181
  26. 8
  27. 5
  28. 9
  29. 6
  30. 264
  31. 438
  32. 169
  33. 5
  34. 459
  35. 41
  36. 261
  37. 7
  38. 183
  39. 97
  40. 30

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