Problems

Replace the letters with numbers (all digits must be different) so that the correct equality is obtained: \(A/ B/ C + D/ E/ F + G/ H/ I = 1\).

The best student in the class, Katie, and the second-best, Mike, tried to find the minimum 5-digit number which consists of different even numbers. Katie found her number correctly, but Mike was mistaken. However, it turned out that the difference between Katie and Mike’s numbers was less than 100. What are Katie and Mike’s numbers?

Decipher the puzzle shown in the diagram.

A three-digit number \(ABB\) is given, the product of the digits of which is a two-digit number \(AC\) and the product of the digits of this number is \(C\) (here, as in mathematical puzzles, the digits in the numbers are replaced by letters where the same letters correspond to the same digits and different letters to different digits). Determine the original number.

A girl chose a 4-letter word and replaced each letter with the corresponding number in the alphabet. The number turned out to be 2091425. What word did she choose?

Replace the question marks with the appropriate letters or words:

a) r, o, y, g, b, ?, ?;

b) a, c, f, j, ?, ?;

c) one, three, five, ?,

d) A, H, I, M, O, T, U, ?, ?, ?, ?;

e) o, t, t, f, f, s, s, e, ?, ?.

In the rebus in the diagram below, the arithmetic operations are carried out from left to right (even though the brackets are not written).

For example, in the first row "\(** \div 5 + * \times 7 = 4*\)" is the same as "\(((** \div 5) +*) \times 7 = 4*\)". Each number in the last row is the sum of the numbers in the column above it. The result of each \(n\)-th row is equal to the sum of the first four numbers in the \(n\)-th column. All of the numbers in this rebus are non-zero and do not begin with a zero, however they could end with a zero. That is, 10 is allowed but not 01 or 0. Solve the rebus.

Decode this rebus: replace the asterisks with numbers such that the equalities in each row are true and such that each number in the bottom row is equal to the sum of the numbers in the column above it.

Decipher the following rebus. Despite the fact that only two figures are known here, and all the others are replaced by asterisks, the question can be restored.

Using five twos, arithmetic operations and exponentiation, form the numbers from 1 to 26.