A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and Histidine will have _________ peptide linkages.

First, recall what a peptide linkage is. A peptide linkage, also called an amide bond, is the covalent bond that forms when the carboxyl group $$\big(-\mathrm{COOH}\big)$$ of one amino acid reacts with the amino group $$\big(-\mathrm{NH_2}\big)$$ of another amino acid, with the elimination of a molecule of water $$\big(\mathrm{H_2O}\big).$$

Whenever amino acids combine linearly to form a peptide, each new bond that joins two neighboring amino-acid residues is precisely one peptide linkage.

Now, let us denote by $$n$$ the total number of individual amino-acid molecules that are being joined. We have the general relationship:

$$\text{Number of peptide linkages}=n-1$$

This statement is easily justified: the first amino acid has a free amino group on one end, and the last amino acid keeps a free carboxyl group on the other end. All the internal joins between successive residues are peptide bonds, and there is exactly one less bond than the number of residues.

In the present problem, the mixture contains one molecule each of Glycine, Leucine, Aspartic acid and Histidine. Therefore,

$$n = 4$$

Substituting this value in the formula stated above, we get

$$\text{Number of peptide linkages} = n - 1 = 4 - 1$$

$$\text{Number of peptide linkages} = 3$$

So, the answer is $$3$$.