Digits in disguise

You have done arithmetic with numbers. How about doing it with LETTERS? In these puzzles each letter stands for a particular digit from 0 to 9, and your job is to work out which.

Start with T + T + T = UT. A one-digit number, added to itself twice, gives a two-digit sum — and the units digit of that sum is the SAME as the single digit being added.

So what could T be? Test it. If T were 2, then 2 + 2 + 2 = 6, which is one digit, not two, and its units digit is not 2. If T were 3, then 3 + 3 + 3 = 9 — again one digit.

Keep going. T = 4 gives 12: two digits, but the units digit is 2, not 4. T = 5 gives 15: two digits, and the units digit IS 5. That works, so T = 5 and UT = 15, which means U = 1.

Here is a second one: K2 + K2 = HMM. Here K2 is a two-digit number with the digit 2 in the units place and K in the tens place, added to itself to give a three-digit sum HMM.

What must M be? The units digit of the sum comes from 2 + 2 = 4, so M = 4 in the units place. But the tens place of the sum is also M, so the tens digits must also produce a 4. And H? Since two two-digit numbers can total at most 198, H can only be 1.

Try the rest yourself — YY + Z = ZOO, B5 + 3D = ED5, KP + KP = PRR, and C1 + C = 1FF — and share how you thought about each with your classmates; you may well find approaches nobody else used. These types of questions are called cryptarithms, or alphametics ('crypt' means hidden — the digits are hiding behind letters). Wherever a letter appears in a puzzle, it stands for the same digit.