Digits in Disguise

Class 7 Maths · Chapter 6: Number Play · NCERT Ganita Prakash section 6.5

Learn

In a cryptarithm, letters stand for digits (each letter one digit). T + T + T = UT: three T's make a 2-digit number ending in T. Try: 3 × 2 = 6, 3 × 4 = 12 … only 3 × 5 = 15 ends in 5. So T = 5 and U = 1.

5 + 5 + 5 = 15

K2 + K2 = HMM. The units: 2 + 2 = 4, so M = 4. Now the tens must also give 4 with a carry into the hundreds: K + K = 14, so K = 7: 72 + 72 = 144, and H = 1. Start from the units column and use what you learn.

72 + 72 = 144

Parity helps too. A bulb is ON and its switch is pressed 77 times: every two presses bring it back, and 77 is odd, so it ends OFF. 50 loose sheets of a book (each with an odd and an even page) have a page total that is even, since 50 odd sums make even.

Leading digits: YY + Z = ZOO. A 2-digit number plus a 1-digit number is at most 99 + 9 = 108, so the 3-digit answer starts with 1: Z = 1. Then YY + 1 = 1OO means YY = 99 and O = 0. Ishaan's tip: a carry into a new place is always 1.

99 + 1 = 100

Explore: crack the code.

1. T + T + T = UT. Set the digit T.
2. K2 + K2 = HMM. Set the digit K.
3. A + A = 1B and B = 6. Set A.

Remember

• In a cryptarithm, start from the units column and keep track of carries.
• A carry into a new place is always 1; parity can rule answers out quickly.

Quick check

In P7 + 2Q = 81, what is P + Q? (P and Q are digits.)

1. 9
2. 8
3. 10
4. 11

Think about it

Solve UT + TA = TAT.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.